# Homework Help: Exp as covering homomorphism for connected Lie group

1. May 16, 2012

### Sajet

1. The problem statement, all variables and given/known data

Let $H$ be a connected Lie group with Lie algebra $\mathfrak h$ such that $[\mathfrak h, \mathfrak h] = 0$. Show that:

$\exp: \mathfrak h \rightarrow H$

is the covering homomorphism.

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I am not really sure what I have to show here, specifically I don't know what they mean by "the covering homomorphism" which to me implies uniqueness but I can't find a theorem which implies that there exists a unique covering homomorphism in the given case.

Or maybe I'm merely supposed to show that this is both a homomorphism and a covering?

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