Algebraic representation

In mathematics, an algebraic representation of a group G on a k-algebra A is a linear representation such that, for each g in G, 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 is an algebraic representation of G.

If A is a commutative G-algebra, then is an affine G-scheme.


  • Claudio Procesi (2007) Lie Groups: an approach through invariants and representation, Springer, ISBN 9780387260402.

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