# Algebraic group representation

From Groupprops

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 representation**of a group is a homomorphism from a group ot the automorphism group of an algebraic variety.m say . If the group already has the structure of an algebraic group, then we require that the map be an algebraic map.

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