A relatively short self-contained proof of the Baker-Campbell-Hausdorff theorem
Rings and Algebras
2020-07-06 v2 Representation Theory
Abstract
We give a new purely algebraic proof of the Baker-Campbell-Hausdorff theorem, which states that the homogeneous components of the formal expansion of are Lie polynomials. Our proof is based on a recurrence formula for these components and a lemma that states that if under certain conditions a commutator of a non-commuting variable and a given polynomial is a Lie polynomial, then the given polynomial itself is a Lie polynomial.
Keywords
Cite
@article{arxiv.2005.00855,
title = {A relatively short self-contained proof of the Baker-Campbell-Hausdorff theorem},
author = {Harald Hofstätter},
journal= {arXiv preprint arXiv:2005.00855},
year = {2020}
}