Hey I'm basically trying to solve exercise 7.12 of Harris & Fulton's first course in representation theory:
if $H \rightarrow G$ is a covering of connected lie groups, show that Z(G) is discrete if and only if Z(H) is discrete.
I was able to prove that Z(G) discrete implies Z(H) discrete, using the fact that $\pi(Z(H)) \subset Z(G)$ (where $\pi$ is the covering), but I'm clueless about the other direction of the equivalence :)
