Let $G$ be a linear algebraic group over a field $K$ of characterstic zero acting on a vector space $V$. Then does this action induce a representation : $$\Gamma : Lie(G) \to gl(V)$$
If yes, how ? Please help me understand this. I would appreciate if the explanation is simple and from all prespectives like thinking of $Lie(G)$ as derivations on the coordinate ring or as the tangent space at identity of $G$.