Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 023, 16 pages      arXiv:2108.11103      https://doi.org/10.3842/SIGMA.2022.023

Post-Lie Magnus Expansion and BCH-Recursion

Mahdi J. Hasan Al-Kaabi a, Kurusch Ebrahimi-Fard b and Dominique Manchon c
a) Mathematics Department, College of Science, Mustansiriyah University, Palestine Street, P.O. Box 14022, Baghdad, Iraq
b) Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
c) Laboratoire de Mathématiques Blaise Pascal, CNRS et Université Clermont-Auvergne (UMR 6620), 3 place Vasarély, CS 60026, F63178 Aubière, France

Received August 26, 2021, in final form March 10, 2022; Published online March 23, 2022

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

Key words: post-Lie algebra; pre-Lie algebra; Rota-Baxter algebra; Magnus expansion; BCH-formula; rooted trees.

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