Post-Lie Magnus expansion and BCH-recursion (Q2120869)

The paper essentially consists into an interesting survey of results about combinatorial and algebraic structures in relation with some well-known formal power series with non-commutative variables, together with a final section with new results. Section 2 deals with post-Lie algebras which are Lie algebras with another bilinear product satisfying some compatibility relations with the Lie product. Section 3 is devoted to the Baxter-Campbell-Hausdorff (BCH) recursion, and its relation with (complete) Rota-Baxter algebras. The authors then describe the Magnus expansion on the free post-Lie algebra on a set, in Section 4. Finally in Section 5, they show that the aforementioned expansion described in Section 4 is the same as the BCH-recursion from Section 3.