Post-Lie Algebras, Factorization Theorems and Isospectral-Flows

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

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