Post-Lie-Magnus expansion and BCH-recursion

Mahdi Jasim Hasan Al-Kaabi (1, 2) , Kurusch Ebrahimi-Fard (3) , Dominique Manchon (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Al-Mustansiriyah University
3 NTNU - Norwegian University of Science and Technology

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.

Mots clés: Post-Lie algebra; pre-Lie algebra; Rota--Baxter algebra; Magnus expansion; BCH-formula; rooted trees.; Rota-Baxter algebra; rooted trees. MSC Classification: 16T05; 16T10; 16T30; 17A30

Domaines: Anneaux et algèbres [math.RA]

Mahdi Jasim Hasan Al-Kaabi, Kurusch Ebrahimi-Fard, Dominique Manchon. Post-Lie-Magnus expansion and BCH-recursion. Symmetry, Integrability and Geometry : Methods and Applications, 2022, 18 (023), 16 p. ⟨hal-03325479v2⟩