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arXiv · 1711.02694

Post-Lie Algebras, Factorization Theorems and Isospectral-Flows

Kurusch Ebrahimi-Fard·Igor Mencattini
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Abstract

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 post-Lie algebra is defined in terms of solutions of modified classical Yang-Baxter equation. In this context, we prove a factorization theorem for group-like elements. An explicit exponential solution of the corresponding Lie bracket flow is presented, which is based on the aforementioned post-Lie Magnus expansion.

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Kurusch Ebrahimi-Fard, Igor Mencattini. 2017-11-07. Post-Lie Algebras, Factorization Theorems and Isospectral-Flows. https://doi.org/10.1007/978-3-030-01397-4

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