# 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.

## References

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

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