This article is cited in 1 paper

Post-Lie Magnus Expansion and BCH-Recursion

Mahdi J. Hasan Al-Kaabi^a, Kurusch Ebrahimi-Fard^b, Dominique Manchon<sup>c

a</sup> 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

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.

Keywords: post-Lie algebra, pre-Lie algebra, Rota–Baxter algebra, Magnus expansion, BCH-formula, rooted trees.

MSC: 16T05, 16T10, 16T30, 17A30

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

Language: English

DOI: 10.3842/SIGMA.2022.023

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ArXiv: 2108.11103