English

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 log(eAeB)\log(e^Ae^B) 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}
}