Lie groups and Lie algebras: Lie's theorem on exponentiating homomorphisms

Описание

We ask when a Lie algebra homomorphism can be exponentiated to give a Lie group homomorphism. We study the example of homomorphisms from U(1) to U(1), and state Lie's theorem which gives us a sufficient condition (simply-connectedness) of G to ensure that any homomorphism f from g to h exponentiates to a homomorphism F from G to H.