The previous lecture in this series is here. The next lecture in this series is here.
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.
This video is part of a lecture course by Richard Borcherds from 2021.