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== Inoltre combinano assistenza alimentare Pandora Joyas ==
{| class="wikitable" style="float:right; clear:right;"
|-
! A \ B
! R
! C
! H
! O
|-
! R
|A<sub>1</sub>
|A<sub>2</sub>
|C<sub>3</sub>
|F<sub>4</sub>
|-
! C
|A<sub>2</sub>
|A<sub>2</sub> × A<sub>2</sub>
|A<sub>5</sub>
|E<sub>6</sub>
|-
! H
|C<sub>3</sub>
|A<sub>5</sub>
|D<sub>6</sub>
|E<sub>7</sub>
|-
! O
|F<sub>4</sub>
|E<sub>6</sub>
|E<sub>7</sub>
|E<sub>8</sub>
|}


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In [[mathematics]], the '''Freudenthal magic square''' (or '''Freudenthal–Tits magic square''') is a construction relating several [[Lie algebra]]s (and their associated [[Lie group]]s). It is named after [[Hans Freudenthal]] and [[Jacques Tits]], who developed the idea independently. It associates a Lie algebra to a pair of division algebras ''A'', ''B''. The resulting Lie algebras have [[Dynkin diagram]]s according to the table at right. The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in ''A'' and ''B'', despite the original construction not being symmetric, though [[#Vinberg's symmetric method|Vinberg's symmetric method]] gives a symmetric construction; it is not a [[magic square]] as in [[recreational mathematics]].
 
  <li>[http://laspaghettata.altervista.org/index.php?option=com_kunena&func=view&catid=11&id=8977&Itemid=15#8977 http://laspaghettata.altervista.org/index.php?option=com_kunena&func=view&catid=11&id=8977&Itemid=15#8977]</li>
 
  <li>[http://www.juegosetnicos.com.ar/spip.php?article87&lang=ru/ http://www.juegosetnicos.com.ar/spip.php?article87&lang=ru/]</li>
 
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</ul>


== In tutto il mondo dei giochi online Lacoste Polo ==
The Freudenthal magic square includes all of the [[exceptional Lie group]]s apart from ''G''<sub>2</sub>, and it provides one possible approach to justify the assertion that "the exceptional Lie groups all exist because of the [[octonions]]": ''G''<sub>2</sub> itself is the [[automorphism group]] of the octonions (also, it is in many ways like a [[classical Lie group]] because it is the stabilizer of a generic 3-form on a 7-dimensional vector space &ndash; see [[prehomogeneous vector space]]).


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==Constructions==
 
See [[#History|history]] for context and motivation. These were originally constructed circa 1958 by Freudenthal and Tits, with more elegant formulations following in later years.<ref name="baez200243" />
  <li>[http://cgi.www5c.biglobe.ne.jp/~kk_aoi/bbs/apeboard_plus.cgi/ http://cgi.www5c.biglobe.ne.jp/~kk_aoi/bbs/apeboard_plus.cgi/]</li>
 
  <li>[http://www.metransparent.com/spip.php?article9653&lang=ar&id_forum=11085/ http://www.metransparent.com/spip.php?article9653&lang=ar&id_forum=11085/]</li>
 
  <li>[http://advertsbook.net/forum/read.php?54,332198 http://advertsbook.net/forum/read.php?54,332198]</li>
 
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</ul>


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===Tits' approach===
Tits' approach, discovered circa 1958 and published in {{Harv|Tits|1966}}, is as follows.


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Associated with any normed real [[division algebra]] ''A'' (i.e., R, C, H or O) there is a [[Jordan algebra]], ''J''<sub>3</sub>(''A''), of 3 × 3 ''A''-[[Hermitian matrices]]. For any pair (''A'', ''B'') of such division algebras, one can define a [[Lie algebra]]
 
 
  <li>[http://metransparent.nfrance.com/~k1001/spip.php?article8359&lang=ar&id_forum=8701/ http://metransparent.nfrance.com/~k1001/spip.php?article8359&lang=ar&id_forum=8701/]</li>
:<math> L=\left (\mathfrak{der}(A)\oplus\mathfrak{der}(J_3(B))\right )\oplus \left (A_0\otimes J_3(B)_0 \right )</math>
 
 
  <li>[http://www.cctv0534.com/forum.php?mod=viewthread&tid=253667 http://www.cctv0534.com/forum.php?mod=viewthread&tid=253667]</li>
where ''der'' denotes the Lie algebra of [[derivation (abstract algebra)|derivation]]s of an algebra, and the subscript 0 denotes the [[trace-free]] part. The Lie algebra ''L'' has <math>\mathfrak{der}(A)\oplus\mathfrak{der}(J_3(B))</math> as a subalgebra, and this acts naturally on <math>A_0\otimes J_3(B)_0</math>. The Lie bracket on <math>A_0\otimes J_3(B)_0</math> (which is not a subalgebra) is not obvious, but Tits showed how it could be defined, and that it produced the following table of [[compact Lie algebra]]s.
 
 
  <li>[http://www.lsfygzs.com/news/html/?191159.html http://www.lsfygzs.com/news/html/?191159.html]</li>
{| class="wikitable"
 
|-
  <li>[http://mlsh.net.cn/forum.php?mod=viewthread&tid=2260887 http://mlsh.net.cn/forum.php?mod=viewthread&tid=2260887]</li>
!
 
! B
  </ul>
! R
! C
! H
! O
|-
! A
! ''der''(A/B)
! 0
! 0
! <math>\mathfrak{sp}_1</math>
! <math>\mathfrak{g}_2</math>
|-
! R
! 0
|<math>\mathfrak{so}_3</math>
|<math>\mathfrak{su}_3</math>
|<math>\mathfrak{sp}_3</math>
|<math>\mathfrak{f}_4</math>
|-
! C
! 0
|<math>\mathfrak{su}_3</math>
|<math>\mathfrak{su}_3\oplus\mathfrak{su}_3</math>
|<math>\mathfrak{su}_6</math>
|<math>\mathfrak{e}_6</math>
|-
! H
! <math>\mathfrak{sp}_1</math>
| <math>\mathfrak{sp}_3</math>
| <math>\mathfrak{su}_6</math>
| <math>\mathfrak{so}_{12}</math>
| <math>\mathfrak{e}_7</math>
|-
! O
! <math>\mathfrak{g}_2</math>
| <math>\mathfrak{f}_4</math>
| <math>\mathfrak{e}_6</math>
| <math>\mathfrak{e}_7</math>
| <math>\mathfrak{e}_8</math>
|}
 
Note that by construction, the row of the table with ''A''='''R''' gives '''der'''(J<sub>3</sub>(''B'')), and similarly vice versa.
 
===Vinberg's symmetric method===
The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in ''A'' and ''B''. This is not obvious from Tits' construction. [[Ernest Vinberg]] gave a construction which is manifestly symmetric, in {{Harv|Vinberg|1966}}. Instead of using a Jordan algebra, he uses an algebra of skew-hermitian trace-free matrices with entries in ''A'' ⊗ ''B'', denoted <math>\mathfrak{sa}_3(A\otimes B)</math>. Vinberg defines a Lie algebra structure on
:<math> \mathfrak{der}(A)\oplus\mathfrak{der}(B)\oplus\mathfrak{sa}_3(A\otimes B).</math>
When ''A'' and ''B'' have no derivations (i.e., '''R''' or '''C'''), this is just the Lie (commutator) bracket on <math>\mathfrak{sa}_3(A\otimes B)</math>. In the presence of derivations, these form a subalgebra acting naturally on <math>\mathfrak{sa}_3(A\otimes B)</math> as in Tits' construction, and the tracefree commutator bracket on <math>\mathfrak{sa}_3(A\otimes B)</math> is modified by an expression with values in <math> \mathfrak{der}(A)\oplus\mathfrak{der}(B)</math>.
 
===Triality===
A more recent construction, due to [[Pierre Ramond]] {{Harv|Ramond|1976}} and Bruce Allison {{Harv|Allison|1978}} and developed by Chris Barton and [[Tony Sudbery|Anthony Sudbery]], uses [[triality]] in the form developed by [[John Frank Adams]]; this was presented in {{Harv|Barton|Sudbery|2000}}, and in streamlined form in {{Harv|Barton|Sudbery|2003}}. Whereas Vinberg's construction is based on the automorphism groups of a division algebra ''A'' (or rather their Lie algebras of derivations), Barton and Sudbery use the group of automorphisms of the corresponding triality. The triality is the trilinear map
:<math> A_1\times A_2\times A_3 \to \mathbf R</math>
obtained by taking three copies of the division algebra ''A'', and using the inner product on ''A'' to dualize the multiplication. The automorphism group is the subgroup of SO(''A''<sub>1</sub>) × SO(''A''<sub>2</sub>) × SO(''A''<sub>3</sub>) preserving this trilinear map. It is denoted Tri(''A''). The following table compares its Lie algebra to the Lie algebra of derivations.
 
{| class="wikitable"
|-
! ''A'':
! '''R'''
! '''C'''
! '''H'''
! '''O'''
|-
! <math>\mathfrak{der}(A)</math>
| 0
| 0
| <math>\mathfrak{sp}_1</math>
| <math>\mathfrak{g}_2</math>
|-
! <math>\mathfrak{tri}(A)</math>
| 0
| <math>\mathfrak u_1 \oplus \mathfrak u_1</math>
| <math>\mathfrak{sp}_1 \oplus \mathfrak{sp}_1\oplus \mathfrak{sp}_1</math>
| <math>\mathfrak{so}_8</math>
|}
 
Barton and Sudbery then identify the magic square Lie algebra corresponding to (''A'',''B'') with a Lie algebra structure on the vector space
:<math> \mathfrak{tri}(A)\oplus\mathfrak{tri}(B)\oplus (A_1\otimes B_1)\oplus (A_2\otimes B_2)\oplus (A_3\otimes B_3). </math>
The Lie bracket is compatible with a '''Z'''<sub>2</sub> × '''Z'''<sub>2</sub> grading, with '''tri'''(''A'') and '''tri'''(''B'') in degree (0,0), and the three copies of ''A'' ⊗ ''B'' in degrees (0,1), (1,0) and (1,1). The bracket preserves '''tri'''(''A'') and '''tri'''(''B'') and these act naturally on the three copies of ''A'' ⊗ ''B'', as in the other constructions, but the brackets between these three copies are more constrained.
 
For instance when ''A'' and ''B'' are the octonions, the triality is that of Spin(8), the double cover of SO(8), and the Barton-Sudbery description yields
:<math>\mathfrak e_8\cong \mathfrak{so}_8\oplus\widehat{\mathfrak{so}}_8\oplus(V\otimes \widehat V)\oplus (S_+\otimes\widehat S_+)\oplus (S_-\otimes \widehat S_-)</math>
where V, S<sub>+</sub> and S<sub>-</sub> are the three 8 dimensional representations of <math>\mathfrak{so}_8</math> (the fundamental representation and the two [[spin representation]]s), and the hatted objects are an isomorphic copy.
 
With respect to one of the '''Z'''<sub>2</sub> gradings, the first three summands combine to give <math>\mathfrak{so}_{16}</math> and the last two together form one of its spin representations Δ<sub>+</sub><sup>128</sup> (the superscript denotes the dimension). This is a well known [[Riemannian symmetric space|symmetric decomposition]] of [[E8 (mathematics)|E8]].
 
The Barton-Sudbery construction extends this to the other Lie algebras in the magic square. In particular, for the exceptional Lie algebras in the last row (or column), the symmetric decompositions are:
:<math>\mathfrak f_4\cong \mathfrak{so}_9\oplus \Delta^{16}</math>
:<math>\mathfrak e_6\cong (\mathfrak{so}_{10}\oplus \mathfrak u_1)\oplus \Delta^{32}</math>
:<math>\mathfrak e_7\cong (\mathfrak{so}_{12}\oplus \mathfrak{sp}_1)\oplus \Delta_+^{64}</math>
:<math>\mathfrak e_8\cong \mathfrak{so}_{16}\oplus \Delta_+^{128}.</math>
 
==Generalizations==
===Split composition algebras===
In addition to the [[normed division algebra]]s, there are other [[composition algebra]]s over '''R''', namely the [[split-complex number]]s, the [[split-quaternions]] and the [[split-octonions]]. If one uses these instead of the complex numbers, quaternions, and octonions, one obtains the following variant of the magic square (where the split versions of the division algebras are denoted by a dash).
 
{| class="wikitable"
|-
! A\B
! R
! C'
! H'
! O'
|-
! R
|<math>\mathfrak{so}_3</math>
|<math>\mathfrak{sl}_3(\mathbf R)</math>
|<math>\mathfrak{sp}_6(\mathbf R)</math>
|<math>\mathfrak{f}_{4(4)}</math>
|-
! C'
|<math>\mathfrak{sl}_3(\mathbf R)</math>
|<math>\mathfrak{sl}_3(\mathbf R)\oplus\mathfrak{sl}_3(\mathbf R)</math>
|<math>\mathfrak{sl}_6(\mathbf R)</math>
|<math>\mathfrak{e}_{6(6)}</math>
|-
! H'
| <math>\mathfrak{sp}_6(\mathbf R)</math>
| <math>\mathfrak{sl}_6(\mathbf R)</math>
| <math>\mathfrak{so}_{6,6}</math>
| <math>\mathfrak{e}_{7(7)}</math>
|-
! O'
| <math>\mathfrak{f}_{4(4)}</math>
| <math>\mathfrak{e}_{6(6)}</math>
| <math>\mathfrak{e}_{7(7)}</math>
| <math>\mathfrak{e}_{8(8)}</math>
|}
Here all the Lie algebras are the [[List of simple Lie groups|split real form]] except for '''so'''<sub>3</sub>, but a sign change in the definition of the Lie bracket can be used to produce the split form '''so'''<sub>2,1</sub>. In particular, for the exceptional Lie algebras, the maximal compact subalgebras are as follows:
{| class="wikitable"
|-
! Split form
| <math>\mathfrak{f}_{4(4)}</math>
| <math>\mathfrak{e}_{6(6)}</math>
| <math>\mathfrak{e}_{7(7)}</math>
| <math>\mathfrak{e}_{8(8)}</math>
|-
! Maximal compact
| <math>\mathfrak{sp}_3\oplus\mathfrak{sp}_1</math>
| <math>\mathfrak{sp}_4</math>
| <math>\mathfrak{su}_8</math>
| <math>\mathfrak{so}_{16}</math>
|}
 
A non-symmetric version of the magic square can also be obtained by combining the split algebras with the usual division algebras. According to Barton and Sudbery, the resulting table of Lie algebras is as follows.
 
{| class="wikitable"
|-
! A\B
! R
! C
! H
! O
|-
! R
|<math>\mathfrak{so}_3</math>
|<math>\mathfrak{su}_3</math>
|<math>\mathfrak{sp}_3</math>
|<math>\mathfrak{f}_{4}</math>
|-
! C'
|<math>\mathfrak{sl}_3(\mathbf R)</math>
|<math>\mathfrak{sl}_3(\mathbf C)</math>
|<math>\mathfrak{sl}_3(\mathbf H)</math>
|<math>\mathfrak{e}_{6(-26)}</math>
|-
! H'
| <math>\mathfrak{sp}_6(\mathbf R)</math>
| <math>\mathfrak{su}_{3,3}</math>
| <math>\mathfrak{so}^*_6(\mathbf H)</math>
| <math>\mathfrak{e}_{7(-25)}</math>
|-
! O'
| <math>\mathfrak{f}_{4(4)}</math>
| <math>\mathfrak{e}_{6(2)}</math>
| <math>\mathfrak{e}_{7(-5)}</math>
| <math>\mathfrak{e}_{8(-24)}</math>
|}
 
The real exceptional Lie algebras appearing here can again be described by their maximal compact subalgebras.
{| class="wikitable"
|-
! Lie algebra
| <math>\mathfrak{e}_{6(2)}</math>
| <math>\mathfrak{e}_{6(-26)}</math>
| <math>\mathfrak{e}_{7(-5)}</math>
| <math>\mathfrak{e}_{7(-25)}</math>
| <math>\mathfrak{e}_{8(-24)}</math>
|-
! Maximal compact
| <math>\mathfrak{su}_6\oplus\mathfrak{sp}_1</math>
| <math>\mathfrak{f}_4</math>
| <math>\mathfrak{su}_{12}\oplus\mathfrak{sp}_1</math>
| <math>\mathfrak{e}_6\oplus\mathfrak{u}_1</math>
| <math>\mathfrak{e}_7\oplus\mathfrak{sp}_1</math>
|}
 
===Arbitrary fields===
The split forms of the composition algebras and Lie algebras can be defined over any [[field (mathematics)|field]] '''K'''. This yields the following magic square.
{| class="wikitable"
|-
|<math>\mathfrak{so}_3(\mathbf K)</math>
|<math>\mathfrak{sl}_3(\mathbf K)</math>
|<math>\mathfrak{sp}_6(\mathbf K)</math>
|<math>\mathfrak{f}_{4}(\mathbf K)</math>
|-
|<math>\mathfrak{sl}_3(\mathbf K)</math>
|<math>\mathfrak{sl}_3(\mathbf K)\oplus\mathfrak{sl}_3(\mathbf K)</math>
|<math>\mathfrak{sl}_6(\mathbf K)</math>
|<math>\mathfrak{e}_{6}(\mathbf K)</math>
|-
| <math>\mathfrak{sp}_6(\mathbf K)</math>
| <math>\mathfrak{sl}_6(\mathbf K)</math>
| <math>\mathfrak{so}_{12}(\mathbf K)</math>
| <math>\mathfrak{e}_{7}(\mathbf K)</math>
|-
| <math>\mathfrak{f}_{4}(\mathbf K)</math>
| <math>\mathfrak{e}_{6}(\mathbf K)</math>
| <math>\mathfrak{e}_{7}(\mathbf K)</math>
| <math>\mathfrak{e}_{8}(\mathbf K)</math>
|}
There is some ambiguity here if '''K''' is not algebraically closed. In the case '''K''' = '''C''', this is the complexification of the Freudenthal magic squares for '''R''' discussed so far.
 
===More general Jordan algebras===
The squares discussed so far are related to the Jordan algebras ''J''<sub>3</sub>(''A''), where ''A'' is a division algebra. There are also Jordan algebras ''J<sub>n</sub>''(''A''), for any positive integer ''n'', as long as ''A'' is associative. These yield split forms (over any field '''K''') and compact forms (over '''R''') of generalized magic squares.
 
{| class="wikitable"
|-
|<math>\mathfrak{so}_n(\mathbf K)</math>
|<math>\mathfrak{sl}_n(\mathbf K)\text{ or }\mathfrak{su}_n</math>
|<math>\mathfrak{sp}_{2n}(\mathbf K)\text{ or }\mathfrak{sp}_n</math>
|-
|<math>\mathfrak{sl}_n(\mathbf K)\text{ or }\mathfrak{su}_n</math>
|<math>\mathfrak{sl}_n(\mathbf K)\oplus\mathfrak{sl}_n(\mathbf K)\text{ or }\mathfrak{su}_n\oplus\mathfrak{su}_n</math>
|<math>\mathfrak{sl}_{2n}(\mathbf K)\text{ or }\mathfrak{su}_{2n}</math>
|-
| <math>\mathfrak{sp}_{2n}(\mathbf K)\text{ or }\mathfrak{sp}_n</math>
| <math>\mathfrak{sl}_{2n}(\mathbf K)\text{ or }\mathfrak{su}_{2n}</math>
| <math>\mathfrak{so}_{4n}(\mathbf K)</math>
|}
 
For ''n''=2, J<sub>''2''</sub>(''O'') is also a Jordan algebra. In the compact case (over '''R''') this yields a magic square of orthogonal Lie algebras.
{| class="wikitable"
|-
! A\B
! R
! C
! H
! O
|-
! R
|<math>\mathfrak{so}_2</math>
|<math>\mathfrak{so}_3</math>
|<math>\mathfrak{so}_5</math>
|<math>\mathfrak{so}_9</math>
|-
! C
|<math>\mathfrak{so}_3</math>
|<math>\mathfrak{so}_4</math>
|<math>\mathfrak{so}_6</math>
|<math>\mathfrak{so}_{10}</math>
|-
! H
| <math>\mathfrak{so}_5</math>
| <math>\mathfrak{so}_6</math>
| <math>\mathfrak{so}_8</math>
| <math>\mathfrak{so}_{12}</math>
|-
! O
| <math>\mathfrak{so}_9</math>
| <math>\mathfrak{so}_{10}</math>
| <math>\mathfrak{so}_{12}</math>
| <math>\mathfrak{so}_{16}</math>
|}
 
The last row and column here are the orthogonal algebra part of the isotropy algebra in the symmetric decomposition of the exceptional Lie algebras mentioned previously.
 
These constructions are closely related to [[hermitian symmetric space]]s &ndash; cf. [[prehomogeneous vector space]]s.
 
===Symmetric spaces===
[[Riemannian symmetric space]]s, both compact and non-compact, can be classified uniformly using a magic square construction, in {{Harv|Huang|Leung|2011}}. The irreducible compact symmetric spaces are, up to finite covers, either a compact simple Lie group, a Grassmannian, a [[Lagrangian Grassmannian]], or a [[double Lagrangian Grassmannian]] of subspaces of <math>(\mathbf A \otimes \mathbf B)^n,</math> for normed division algebras '''A''' and '''B'''. A similar construction produces the irreducible non-compact symmetric spaces.
 
==History==
===Rosenfeld projective planes===
Following [[Ruth Moufang]]'s discovery in 1933 of the [[Cayley projective plane]] or "octonionic projective plane" '''P'''<sup>2</sup>('''O'''), whose symmetry group is the exceptional Lie group [[F4 (mathematics)|F<sub>4</sub>]], and with the knowledge that [[G2 (mathematics)|''G''<sub>2</sub>]] is the automorphism group of the octonions, it was proposed by {{harvtxt|Rozenfeld|1956}} that the remaining exceptional Lie groups [[E6 (mathematics)|''E''<sub>6</sub>]], [[E7 (mathematics)|''E''<sub>7</sub>]], and [[E8 (mathematics)|E<sub>8</sub>]] are isomorphism groups of projective planes over certain algebras over the octonions:<ref name="baez200243">{{Harv|Baez|2002|loc=[http://math.ucr.edu/home/baez/octonions/node16.html 4.3 The Magic Square]}}</ref>
* the '''{{visible anchor|bioctonions}}''', '''C''' ⊗ '''O''',
* the '''{{visible anchor|quateroctonions}}''', '''H''' ⊗ '''O''',
* the '''{{visible anchor|octooctonions}}''', '''O''' ⊗ '''O'''.
This proposal is appealing, as there are certain exceptional compact [[Riemannian symmetric space]]s with the desired symmetry groups and whose dimension agree with that of the putative projective planes (dim('''P'''<sup>2</sup>('''K''' ⊗ '''K'''′)) = 2dim('''K''')dim('''K'''′)), and this would give a uniform construction of the exceptional Lie groups as symmetries of naturally occurring objects (i.e., without an a priori knowledge of the exceptional Lie groups). The Riemannian symmetric spaces were classified by Cartan in 1926 (Cartan's labels are used in sequel); see [[Riemannian symmetric space#Classification of Riemannian symmetric spaces|classification]] for details, and the relevant spaces are:
* the [[octonionic projective plane]] – FII, dimension 16 = 2 × 8, F<sub>4</sub> symmetry, [[Cayley projective plane]] '''P'''<sup>2</sup>('''O'''),
* the bioctonionic projective plane – EIII, dimension 32 = 2 × 2 × 8, E<sub>6</sub> symmetry, complexified Cayley projective plane, '''P'''<sup>2</sup>('''C''' ⊗ '''O'''),
* the "'''{{visible anchor|quateroctonionic projective plane}}'''"<ref name="baez200245">{{Harv|Baez|2002|loc=[http://math.ucr.edu/home/baez/octonions/node18.html 4.5 '''E'''<sub>7</sub>]}}</ref> – EVI, dimension 64 = 2 × 4 × 8, E<sub>7</sub> symmetry, '''P'''<sup>2</sup>('''H''' ⊗ '''O'''),
* the "'''{{visible anchor|octooctonionic projective plane}}'''"<ref name="baez200246">{{Harv|Baez|2002|loc= [http://math.ucr.edu/home/baez/octonions/node19.html 4.6 '''E'''<sub>8</sub>]}}</ref> – EVIII, dimension 128 = 2 × 8 × 8, E<sub>8</sub> symmetry, '''P'''<sup>2</sup>('''O''' ⊗ '''O''').
The difficulty with this proposal is that while the octonions are a division algebra, and thus a projective plane is defined over them, the bioctonions, quateroctonions and octooctonions are not division algebras, and thus the usual definition of a projective plane does not work. This can be resolved for the bioctonions, with the resulting projective plane being the complexified Cayley plane, but the constructions do not work for the quateroctonions and octooctonions, and the spaces in question do not obey the usual axioms of projective planes,<ref name="baez200243" /> hence the quotes on "(putative) projective plane". However, the tangent space at each point of these spaces can be identified with the plane ('''H''' ⊗ '''O''')<sup>2</sup>, or ('''O''' ⊗ '''O''')<sup>2</sup> further justifying the intuition that these are a form of generalized projective plane.<ref name="baez200245" /><ref name="baez200246" /> Accordingly, the resulting spaces are sometimes called '''Rosenfeld projective planes''' and notated as if they were projective planes. More broadly, these compact forms are the '''Rosenfeld elliptic projective planes''', while the dual non-compact forms are the '''Rosenfeld hyperbolic projective planes'''. A more modern presentation of Rosenfeld's ideas is in {{Harv|Rosenfeld|1997}}, while a brief note on these "planes" is in {{Harv|Besse|1987|loc=pp. 313–316}}.<ref>"[http://math.ucr.edu/home/baez/twf_ascii/week106 This Week's Finds in Mathematical Physics - Week 106]", [[John Baez]] July 23, 1997</ref>
 
The spaces can be constructed using Tit's theory of buildings, which allows one to construct a geometry with any given algebraic group as symmetries, but this requires starting with the Lie groups and constructing a geometry from them, rather than constructing a geometry independently of a knowledge of the Lie groups.<ref name="baez200243" />
 
===Magic square===
While at the level of manifolds and Lie groups, the construction of the projective plane '''P'''<sup>2</sup>('''K''' ⊗ '''K'''′) of two normed division algebras does not work, the corresponding construction at the level of Lie algebras ''does'' work. That is, if one decomposes the Lie algebra of infinitesimal isometries of the projective plane '''P'''<sup>2</sup>('''K''') and applies the same analysis to '''P'''<sup>2</sup>('''K''' ⊗ '''K'''′), one can use this decomposition, which holds when '''P'''<sup>2</sup>('''K''' ⊗ '''K'''′) can actually be defined as a projective plane, as a ''definition'' of a "magic square Lie algebra" ''M''('''K''','''K'''′) This definition is purely algebraic, and holds even without assuming the existence of the corresponding geometric space. This was done independently circa 1958 in {{Harv|Tits|1966}} and by Freudenthal in a series of 11 papers, starting with {{Harv|Freudenthal|1954}} and ending with {{Harv|Freudenthal|1963}}, though the simplified construction outlined here is due to {{Harv|Vinberg|1966}}.<ref name="baez200243" />
 
==See also==
* [[E8 (mathematics)]]
* [[E7 (mathematics)]]
* [[E6 (mathematics)]]
* [[F4 (mathematics)]]
* [[G2 (mathematics)]]
* [[Jordan triple system]]
* [[Euclidean Hurwitz algebra]]
* [[Euclidean Jordan algebra]]
 
==References==
{{reflist}}
{{refbegin}}
* {{cite isbn|0226005275}}
* {{cite journal | ref=harv | first=B.N. |last=Allison | title=Structurable Algebras  |journal= Math. Ann. |volume= 237 |year = 1978 |pages = 133}}
* {{cite doi|10.1090/S0273-0979-01-00934-X}} – [http://math.ucr.edu/home/baez/octonions/node16.html 4.3: The Magic Square]
* {{cite doi|10.1090/S0273-0979-05-01052-9}}
* {{cite arXiv |last1=Barton |first1= C. H. |last2=Sudbery |first2=A. |eprint=math/0001083 |title=Magic Squares of Lie Algebras |year=2000 |version= |accessdate=2012-11-23 }}
* {{cite doi|10.1016/S0001-8708(03)00015-X}}
* {{cite isbn|9783540152798}}
* {{cite journal |ref=harv |first=Hans |last=Freudenthal |authorlink=Hans Freudenthal | journal = Indagationes Math. | language = German | year = 1954 | volume = 16 | title = Beziehungen der E<sub>7</sub> und E<sub>8</sub> zur  Oktavenebene. I | pages = 218–230 | mr = 0063358 }}
* {{cite journal |ref=harv |first=Hans |last=Freudenthal |authorlink=Hans Freudenthal | journal = Indagationes Math. | language = German | year = 1954 | volume = 16 | title = Beziehungen der E<sub>7</sub> und E<sub>8</sub> zur Oktavenebene. II | pages = 363–368 | mr = 0068549 }}
* {{cite journal |ref=harv |first=Hans |last=Freudenthal |authorlink=Hans Freudenthal | journal = Indagationes Math. | language = German | year = 1955 | volume = 17 | title = Beziehungen der E<sub>7</sub> und E<sub>8</sub> zur Oktavenebene. III | pages = 151–157 | mr = 0068550 }}
* {{cite journal |ref=harv |first=Hans |last=Freudenthal |authorlink=Hans Freudenthal | journal = Indagationes Math. | language = German | year = 1955 | volume = 17 | title = Beziehungen der E<sub>7</sub> und E<sub>8</sub> zur Oktavenebene. IV | pages = 277–285 | mr = 0068551 }}
* {{cite journal |ref=harv |first=Hans |last=Freudenthal |authorlink=Hans Freudenthal | journal = Indagationes Math. | language = German | year = 1959 | volume = 21 | title = Beziehungen der E<sub>7</sub> und E<sub>8</sub> zur Oktavenebene. V - IX | pages = 165–201, 447–474| mr = }}
* {{cite journal |ref=harv |first=Hans |last=Freudenthal |authorlink=Hans Freudenthal | journal = Indagationes Math. | language = German | year = 1963 | volume = 25 | title = Beziehungen der E<sub>7</sub> und E<sub>8</sub> zur Oktavenebene. X, XI | pages = 457–471, 472–487 | mr = 0163203 }}
*{{citation|last=Freudenthal|first=Hans|title=Oktaven, Ausnahmegruppen und Oktavengeometrie|year=1951|
publisher= Mathematisch Instituut der Rijksuniversiteit te Utrecht}}
*{{citation|last=Freudenthal|first=Hans|title=Oktaven, Ausnahmegruppen und Oktavengeometrie|journal= Geom. Dedicata|volume=19|year=1985|
pages=7–63|url=http://link.springer.com/article/10.1007%2FBF00233101}} (reprint of 1951 article)
* {{cite doi|10.1007/s00208-010-0549-8}}
* {{cite doi|10.1006/jabr.2000.8697}}
*{{citation|last=Postnikov|first=M.|title= Lie groups and Lie algebras. Lectures in geometry. Semester V |publisher=[[Mir Publishers|Mir]]|year= 1986}}
* [[Pierre Ramond]] (1976), ''[http://inspirehep.net/record/111550 Introduction to Exceptional Lie Groups and Algebras]'', CALT-68-577, California Institute of Technology, Pasadena.
* {{cite journal |ref=harv |last=Rozenfeld |first=Boris A. |title= [Geometrical interpretation of compact simple Lie groups of class ''E''] |language=Russian |journal=Dokl. Akad. Nauk SSSR |volume=106 |year=1956 |pages=600–603 }}
* {{cite isbn|0792343905}}
* {{cite journal | ref=harv | first=Jacques |last=Tits |authorlink=Jacques Tits | title=Algèbres alternatives, algèbres de Jordan et algèbres de Lie exceptionnelles |trans_title = Alternative algebras, Jordan algebras and exceptional Lie algebras |journal= Indagationes Math. | language = French | volume=28 |year=1966 |pages=223–237 |mr = 0219578 }}
* {{cite journal | ref=harv | first=E.B. |last=Vinberg |title=[Construction of the exceptional simple Lie algebras] |journal= Trudy Sem. Vekt. Tenz. Anal. |language = Russian | volume=13 |year=1966 |pages=7-9}}
* {{cite journal | ref=harv | first=E.B. |last=Vinberg | title=Construction of the exceptional simple Lie algebras  |journal= Amer. Math. Soc. Transl. |volume= 213 |year = 2005 |pages = 241-242}}
  {{refend}}
 
[[Category:Lie groups]]
[[Category:Representation theory]]

Latest revision as of 20:06, 30 April 2013

A \ B R C H O
R A1 A2 C3 F4
C A2 A2 × A2 A5 E6
H C3 A5 D6 E7
O F4 E6 E7 E8

In mathematics, the Freudenthal magic square (or Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated Lie groups). It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently. It associates a Lie algebra to a pair of division algebras A, B. The resulting Lie algebras have Dynkin diagrams according to the table at right. The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in A and B, despite the original construction not being symmetric, though Vinberg's symmetric method gives a symmetric construction; it is not a magic square as in recreational mathematics.

The Freudenthal magic square includes all of the exceptional Lie groups apart from G2, and it provides one possible approach to justify the assertion that "the exceptional Lie groups all exist because of the octonions": G2 itself is the automorphism group of the octonions (also, it is in many ways like a classical Lie group because it is the stabilizer of a generic 3-form on a 7-dimensional vector space – see prehomogeneous vector space).

Constructions

See history for context and motivation. These were originally constructed circa 1958 by Freudenthal and Tits, with more elegant formulations following in later years.[1]

Tits' approach

Tits' approach, discovered circa 1958 and published in Template:Harv, is as follows.

Associated with any normed real division algebra A (i.e., R, C, H or O) there is a Jordan algebra, J3(A), of 3 × 3 A-Hermitian matrices. For any pair (A, B) of such division algebras, one can define a Lie algebra

L=(der(A)der(J3(B)))(A0J3(B)0)

where der denotes the Lie algebra of derivations of an algebra, and the subscript 0 denotes the trace-free part. The Lie algebra L has der(A)der(J3(B)) as a subalgebra, and this acts naturally on A0J3(B)0. The Lie bracket on A0J3(B)0 (which is not a subalgebra) is not obvious, but Tits showed how it could be defined, and that it produced the following table of compact Lie algebras.

B R C H O
A der(A/B) 0 0 sp1 g2
R 0 so3 su3 sp3 f4
C 0 su3 su3su3 su6 e6
H sp1 sp3 su6 so12 e7
O g2 f4 e6 e7 e8

Note that by construction, the row of the table with A=R gives der(J3(B)), and similarly vice versa.

Vinberg's symmetric method

The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in A and B. This is not obvious from Tits' construction. Ernest Vinberg gave a construction which is manifestly symmetric, in Template:Harv. Instead of using a Jordan algebra, he uses an algebra of skew-hermitian trace-free matrices with entries in AB, denoted sa3(AB). Vinberg defines a Lie algebra structure on

der(A)der(B)sa3(AB).

When A and B have no derivations (i.e., R or C), this is just the Lie (commutator) bracket on sa3(AB). In the presence of derivations, these form a subalgebra acting naturally on sa3(AB) as in Tits' construction, and the tracefree commutator bracket on sa3(AB) is modified by an expression with values in der(A)der(B).

Triality

A more recent construction, due to Pierre Ramond Template:Harv and Bruce Allison Template:Harv and developed by Chris Barton and Anthony Sudbery, uses triality in the form developed by John Frank Adams; this was presented in Template:Harv, and in streamlined form in Template:Harv. Whereas Vinberg's construction is based on the automorphism groups of a division algebra A (or rather their Lie algebras of derivations), Barton and Sudbery use the group of automorphisms of the corresponding triality. The triality is the trilinear map

A1×A2×A3R

obtained by taking three copies of the division algebra A, and using the inner product on A to dualize the multiplication. The automorphism group is the subgroup of SO(A1) × SO(A2) × SO(A3) preserving this trilinear map. It is denoted Tri(A). The following table compares its Lie algebra to the Lie algebra of derivations.

A: R C H O
der(A) 0 0 sp1 g2
tri(A) 0 u1u1 sp1sp1sp1 so8

Barton and Sudbery then identify the magic square Lie algebra corresponding to (A,B) with a Lie algebra structure on the vector space

tri(A)tri(B)(A1B1)(A2B2)(A3B3).

The Lie bracket is compatible with a Z2 × Z2 grading, with tri(A) and tri(B) in degree (0,0), and the three copies of AB in degrees (0,1), (1,0) and (1,1). The bracket preserves tri(A) and tri(B) and these act naturally on the three copies of AB, as in the other constructions, but the brackets between these three copies are more constrained.

For instance when A and B are the octonions, the triality is that of Spin(8), the double cover of SO(8), and the Barton-Sudbery description yields

e8so8so^8(VV^)(S+S^+)(SS^)

where V, S+ and S- are the three 8 dimensional representations of so8 (the fundamental representation and the two spin representations), and the hatted objects are an isomorphic copy.

With respect to one of the Z2 gradings, the first three summands combine to give so16 and the last two together form one of its spin representations Δ+128 (the superscript denotes the dimension). This is a well known symmetric decomposition of E8.

The Barton-Sudbery construction extends this to the other Lie algebras in the magic square. In particular, for the exceptional Lie algebras in the last row (or column), the symmetric decompositions are:

f4so9Δ16
e6(so10u1)Δ32
e7(so12sp1)Δ+64
e8so16Δ+128.

Generalizations

Split composition algebras

In addition to the normed division algebras, there are other composition algebras over R, namely the split-complex numbers, the split-quaternions and the split-octonions. If one uses these instead of the complex numbers, quaternions, and octonions, one obtains the following variant of the magic square (where the split versions of the division algebras are denoted by a dash).

A\B R C' H' O'
R so3 sl3(R) sp6(R) f4(4)
C' sl3(R) sl3(R)sl3(R) sl6(R) e6(6)
H' sp6(R) sl6(R) so6,6 e7(7)
O' f4(4) e6(6) e7(7) e8(8)

Here all the Lie algebras are the split real form except for so3, but a sign change in the definition of the Lie bracket can be used to produce the split form so2,1. In particular, for the exceptional Lie algebras, the maximal compact subalgebras are as follows:

Split form f4(4) e6(6) e7(7) e8(8)
Maximal compact sp3sp1 sp4 su8 so16

A non-symmetric version of the magic square can also be obtained by combining the split algebras with the usual division algebras. According to Barton and Sudbery, the resulting table of Lie algebras is as follows.

A\B R C H O
R so3 su3 sp3 f4
C' sl3(R) sl3(C) sl3(H) e6(26)
H' sp6(R) su3,3 so6*(H) e7(25)
O' f4(4) e6(2) e7(5) e8(24)

The real exceptional Lie algebras appearing here can again be described by their maximal compact subalgebras.

Lie algebra e6(2) e6(26) e7(5) e7(25) e8(24)
Maximal compact su6sp1 f4 su12sp1 e6u1 e7sp1

Arbitrary fields

The split forms of the composition algebras and Lie algebras can be defined over any field K. This yields the following magic square.

so3(K) sl3(K) sp6(K) f4(K)
sl3(K) sl3(K)sl3(K) sl6(K) e6(K)
sp6(K) sl6(K) so12(K) e7(K)
f4(K) e6(K) e7(K) e8(K)

There is some ambiguity here if K is not algebraically closed. In the case K = C, this is the complexification of the Freudenthal magic squares for R discussed so far.

More general Jordan algebras

The squares discussed so far are related to the Jordan algebras J3(A), where A is a division algebra. There are also Jordan algebras Jn(A), for any positive integer n, as long as A is associative. These yield split forms (over any field K) and compact forms (over R) of generalized magic squares.

son(K) sln(K) or sun sp2n(K) or spn
sln(K) or sun sln(K)sln(K) or sunsun sl2n(K) or su2n
sp2n(K) or spn sl2n(K) or su2n so4n(K)

For n=2, J2(O) is also a Jordan algebra. In the compact case (over R) this yields a magic square of orthogonal Lie algebras.

A\B R C H O
R so2 so3 so5 so9
C so3 so4 so6 so10
H so5 so6 so8 so12
O so9 so10 so12 so16

The last row and column here are the orthogonal algebra part of the isotropy algebra in the symmetric decomposition of the exceptional Lie algebras mentioned previously.

These constructions are closely related to hermitian symmetric spaces – cf. prehomogeneous vector spaces.

Symmetric spaces

Riemannian symmetric spaces, both compact and non-compact, can be classified uniformly using a magic square construction, in Template:Harv. The irreducible compact symmetric spaces are, up to finite covers, either a compact simple Lie group, a Grassmannian, a Lagrangian Grassmannian, or a double Lagrangian Grassmannian of subspaces of (AB)n, for normed division algebras A and B. A similar construction produces the irreducible non-compact symmetric spaces.

History

Rosenfeld projective planes

Following Ruth Moufang's discovery in 1933 of the Cayley projective plane or "octonionic projective plane" P2(O), whose symmetry group is the exceptional Lie group F4, and with the knowledge that G2 is the automorphism group of the octonions, it was proposed by Template:Harvtxt that the remaining exceptional Lie groups E6, E7, and E8 are isomorphism groups of projective planes over certain algebras over the octonions:[1]

This proposal is appealing, as there are certain exceptional compact Riemannian symmetric spaces with the desired symmetry groups and whose dimension agree with that of the putative projective planes (dim(P2(KK′)) = 2dim(K)dim(K′)), and this would give a uniform construction of the exceptional Lie groups as symmetries of naturally occurring objects (i.e., without an a priori knowledge of the exceptional Lie groups). The Riemannian symmetric spaces were classified by Cartan in 1926 (Cartan's labels are used in sequel); see classification for details, and the relevant spaces are:

The difficulty with this proposal is that while the octonions are a division algebra, and thus a projective plane is defined over them, the bioctonions, quateroctonions and octooctonions are not division algebras, and thus the usual definition of a projective plane does not work. This can be resolved for the bioctonions, with the resulting projective plane being the complexified Cayley plane, but the constructions do not work for the quateroctonions and octooctonions, and the spaces in question do not obey the usual axioms of projective planes,[1] hence the quotes on "(putative) projective plane". However, the tangent space at each point of these spaces can be identified with the plane (HO)2, or (OO)2 further justifying the intuition that these are a form of generalized projective plane.[2][3] Accordingly, the resulting spaces are sometimes called Rosenfeld projective planes and notated as if they were projective planes. More broadly, these compact forms are the Rosenfeld elliptic projective planes, while the dual non-compact forms are the Rosenfeld hyperbolic projective planes. A more modern presentation of Rosenfeld's ideas is in Template:Harv, while a brief note on these "planes" is in Template:Harv.[4]

The spaces can be constructed using Tit's theory of buildings, which allows one to construct a geometry with any given algebraic group as symmetries, but this requires starting with the Lie groups and constructing a geometry from them, rather than constructing a geometry independently of a knowledge of the Lie groups.[1]

Magic square

While at the level of manifolds and Lie groups, the construction of the projective plane P2(KK′) of two normed division algebras does not work, the corresponding construction at the level of Lie algebras does work. That is, if one decomposes the Lie algebra of infinitesimal isometries of the projective plane P2(K) and applies the same analysis to P2(KK′), one can use this decomposition, which holds when P2(KK′) can actually be defined as a projective plane, as a definition of a "magic square Lie algebra" M(K,K′) This definition is purely algebraic, and holds even without assuming the existence of the corresponding geometric space. This was done independently circa 1958 in Template:Harv and by Freudenthal in a series of 11 papers, starting with Template:Harv and ending with Template:Harv, though the simplified construction outlined here is due to Template:Harv.[1]

See also

References

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    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
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  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 (reprint of 1951 article)
  • Template:Cite doi
  • Template:Cite doi
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Pierre Ramond (1976), Introduction to Exceptional Lie Groups and Algebras, CALT-68-577, California Institute of Technology, Pasadena.
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • Template:Cite isbn
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
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