Algebraic representation

Not to be confused with algebra representation.

In mathematics, an algebraic representation of a group G on a k-algebra A is a linear representation $\pi :G\to GL(A)$ such that, for each g in G, $\pi (g)$ 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 $T(A)$ is an algebraic representation of G.

If A is a commutative G-algebra, then $\operatorname {Spec} (A)$ is an affine G-scheme.

References

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