acting on a vector space
[1] Cases of particular importance are for Γ a finite group (in the theory of Molien series, in particular), a compact group, a Lie group or algebraic group.
For a basis-independent definition of 'polynomial' nothing is lost by referring to the symmetric powers of the given linear representation of Γ.
[2] This article incorporates material from Invariant polynomial on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
This commutative algebra-related article is a stub.