Projected dynamical system: Difference between revisions

Latest revision as of 01:27, 13 May 2013

In mathematics, in the representation theory of algebraic groups, a linear representation of an algebraic group is said to be rational if, viewed as a map from the group to the general linear group, it is a rational map of algebraic varieties.

Finite direct sums and products of rational representations are rational.

A rational $G$ module is a module that can be expressed as a sum (not necessarily direct) of rational representations.

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+In [[mathematics]], in the [[representation theory]] of [[algebraic group]]s, a [[linear representation]] of an algebraic group is said to be '''rational''' if, viewed as a map from the group to the general linear group, it is a rational map of algebraic varieties.
+Finite direct sums and products of rational representations are rational.
+A rational <math>G</math> module is a module that can be expressed as a sum (not necessarily direct) of rational representations.
+{{see|Group representation}}
+==References==
+* [http://www.jstor.org/view/00029327/di994362/99p00143/ Extensions of Representations of Algebraic Linear Groups]
+* [http://www.encyclopediaofmath.org/index.php/Rational_representation Springer Online Reference Works: Rational Representation]
+[[Category:Representation theory of algebraic groups]]
+{{algebra-stub}}