# Post-Lie Algebras, Factorization Theorems and Isospectral-Flows

@article{EbrahimiFard2017PostLieAF, title={Post-Lie Algebras, Factorization Theorems and Isospectral-Flows}, author={Kurusch Ebrahimi-Fard and Igor Mencattini}, journal={arXiv: Mathematical Physics}, year={2017} }

In these notes we review and further explore the Lie enveloping algebra of a post-Lie algebra. From a Hopf algebra point of view, one of the central results, which will be recalled in detail, is the existence of a second Hopf algebra structure. By comparing group-like elements in suitable completions of these two Hopf algebras, we derive a particular map which we dub post-Lie Magnus expansion. These results are then considered in the case of Semenov-Tian-Shansky's double Lie algebra, where a…

## 8 Citations

### Crossed morphisms, integration of post-Lie algebras and the post-Lie Magnus expansion

- Mathematics
- 2020

Abstract This letter is divided in two parts. In the first one it will be shown that the datum of a post-Lie product is equivalent to the one of an invertible crossed morphism between two Lie…

### From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras

- Mathematics
- 2019

Gian-Carlo Rota mentioned in one of his last articles the problem of developing a theory around the notion of integration algebras, which should be dual to the one of differential algebras. This idea…

### Cohomologies and deformations of modified $r$-matrices

- Mathematics
- 2022

Modified r-matrices are solutions of the modified classical Yang-Baxter equation, introduced by Semenov-Tian-Shansky, and play important roles in mathematical physics. In this paper, first we…

### On the post-symmetric brace algebras

- Mathematics
- 2019

In this paper we identify the post-Lie analogue of the symmetric brace algebras, advocate their role in the theory of the associated D-algebras and present some relations with the so-called post-Lie…

### The Magnus expansion and post-Lie algebras

- MathematicsMath. Comput.
- 2020

The classical and post-Lie Magnus expansions are related and algebraic and geometric arguments allow to placing the classical Magnus expansion in the context of Lie group integrators.

### What Is a Post-Lie Algebra and Why Is It Useful in Geometric Integration

- MathematicsLecture Notes in Computational Science and Engineering
- 2019

We explain the notion of a post-Lie algebra and outline its role in the theory of Lie group integrators.

### Post-Lie-Magnus expansion and BCH-recursion

- Physics
- 2021

. We identify the Baker–Campbell–Hausdorff recursion driven by a weight λ = 1 Rota–Baxter operator with the Magnus expansion relative to the post-Lie structure naturally associated to the…

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