Algebraic group representation

This article describes a notion of representation, or a group action on a certain kind of object.
View a complete list of types of representations

Definition

An algebraic group representationof a group $G$ is a homomorphism from a group $G$ ot the automorphism group of an algebraic variety.m say $V$. If the group already has the structure of an algebraic group, then we require that the map $G\times V\to V$ be an algebraic map.

Note that any linear representation over a field automatically becomes an algebraic group representation.