Algebraic group representation

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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.