Let $G$ be a simply connected Lie group. Is it true that any finite dimensional representation of its Lie algebra is the differential of a representation of $G$?


A reference would be helpful.


Sorry if the question is too basic.



Representations of simply connected Lie groups
A finite-dimensional representation of a Lie algebra is in particular a homomorphism of finite-dimensional Lie algebras. Hence your question is answered in the affirmative e.g. by Th. 3.27 in F. Warner's book "Foundations of differential geometry and Lie groups".


