Английская Википедия:Algebraic representation
Материал из Онлайн справочника
Шаблон:Distinguish Шаблон:Short description In mathematics, an algebraic representation of a group G on a k-algebra A is a linear representation <math>\pi: G \to GL(A)</math> such that, for each g in G, <math>\pi(g)</math> is an algebra automorphism. Equipped with such a representation, the algebra A is then called a G-algebra.
For example, if V is a linear representation of a group G, then the representation put on the tensor algebra <math>T(A)</math> is an algebraic representation of G.
If A is a commutative G-algebra, then <math>\operatorname{Spec}(A)</math> is an affine G-scheme.
See also
References
- Claudio Procesi (2007) Lie Groups: an approach through invariants and representation, Springer, Шаблон:Isbn.
