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Exp as covering homomorphism for connected Lie group

  1. May 16, 2012 #1
    1. The problem statement, all variables and given/known data

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

    [itex]\exp: \mathfrak h \rightarrow H[/itex]

    is the covering homomorphism.

    ---------

    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?
     
  2. jcsd
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