# Homomorphism between Lie groups

Hello I've been reading some Group theory texts and would like to clarify something.
Let's say we have two Lie groups A and B, with corresponding Lie algebras a and b.
Does the fact that a and b share the same Lie Bracket structure, as in if we can find a map
M:a->b which obeys [M(q),M(p)]=M([q,p]), mean that the two corresponding Lie groups are homomorphic to each other? (Due to the BCH formula)