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arXiv · 2005.00855

A relatively short self-contained proof of the Baker-Campbell-Hausdorff theorem

Harald Hofstätter
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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 $\log(e^Ae^B)$ 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.

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Harald Hofstätter. 2020-05-02. A relatively short self-contained proof of the Baker-Campbell-Hausdorff theorem. https://doi.org/10.1016/j.exmath.2020.05.003

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