Post-Lie-Magnus expansion and BCH-recursion

TL;DR

This paper establishes a connection between the Baker-Campbell-Hausdorff recursion driven by a Rota-Baxter operator and the Magnus expansion within the framework of post-Lie algebras, providing new insights into their algebraic structures.

Contribution

It identifies the BCH recursion with the Magnus expansion in the context of post-Lie algebras associated to Rota-Baxter algebras, revealing a novel algebraic relationship.

Findings

BCH recursion driven by Rota-Baxter operator is equivalent to Magnus expansion in post-Lie algebra context

Provides a review of post-Lie Magnus expansion and BCH-recursion

Main result links Rota-Baxter algebra structures with classical Lie algebra expansions

Abstract

We identify the Baker-Campbell-Hausdorff recursion driven by a weight$\lambda=1$ Rota-Baxter operator with the Magnus expansion relativeto the post-Lie structure naturally associated to the correspondingRota-Baxter algebra. Post-Lie Magnus expansion and BCH-recursionare reviewed before the proof of the main result.