Rational representation
From Wikipedia, the free encyclopedia
Further information: Group representation
This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations . Please help improve this article by introducing more precise citations. (May 2024) (Learn how and when to remove this message)
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 {\displaystyle G} module is a module that can be expressed as a sum (not necessarily direct) of rational representations.
References
[edit ]- Bialynicki-Birula, A.; Hochschild, G.; Mostow, G. D. (1963). "Extensions of Representations of Algebraic Linear Groups". American Journal of Mathematics . 85 (1). Johns Hopkins University Press: 131–44. doi:10.2307/2373191. ISSN 1080-6377. JSTOR 2373191.
- Springer Online Reference Works: Rational Representation
