Algebraic group representation

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.