Lie groups: Baker Campbell Hausdorff formula
Channel: Richard E Borcherds
Date: 2021-02-18

This lecture is part of an online graduate course on Lie groups.

We state the Baker Campbell Hausdorff formula for exp(A)exp(B). As applications we show that a Lie group is determined up to local isomorphism by its Lie algebra, and homomorphisms from a simply connected Lie group are determined by homomorphisms from its Lie algebra. We show how to prove the BCH formula using primitive elements of the Hopf algebra of non-commutative power series. Finally we display an explicit form of the BCH formula. 



For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53RWBkiHKoOsTw-dGHAoJ-h