Given a representation of an algebraic group $$\Gamma: G \to GL(V)$$ If we take the differential of $\Gamma$ at $e$, we get $$\Gamma^*: Lie(G) \to gl(V)$$ Suppose that $\Gamma^*$ turns out to be an irreducible and faithful representation. Then does that imply that $\Gamma$ has a finite kernel ? Also, is $\Gamma$ irreducible representation. I would appreciate if a small proof quoting results from a text is given as an answer. Any comments are also welcome !