Let $G$ be a simply connected algebraic group over $C$. We know that a representation of an algebraic group $$\phi : G \to GL(V)$$
induces a representation of its lie algebra (taking the differential of this map $\phi$) .
Now, if $G$ is simply connected and we are given a representation $$\psi : Lie(G) \to gl(W)$$
Is that true that this induces a representation of the group $G$ ? This fact comes up in a paper I am reading and I am not able to realise it.
Please help me in realising how the simple connectedness is used here to get the representation of the group itsef.