Rota-Baxter operators and post-Lie algebra structures on semisimple Lie algebras.
Clicks: 152
ID: 72142
2019
Rota-Baxter operators of weight 1 on are in bijective correspondence to post-Lie algebra structures on pairs , where is complete. We use such Rota-Baxter operators to study the existence and classification of post-Lie algebra structures on pairs of Lie algebras , where is semisimple. We show that for semisimple and , with or simple, the existence of a post-Lie algebra structure on such a pair implies that and are isomorphic, and hence both simple. If is semisimple, but is not, it becomes much harder to classify post-Lie algebra structures on , or even to determine the Lie algebras which can arise. Here only the case was studied. In this paper, we determine all Lie algebras such that there exists a post-Lie algebra structure on with .
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| Authors | Burde, Dietrich;Gubarev, Vsevolod; |
| Journal | communications in algebra |
| Year | 2019 |
| DOI | 10.1080/00927872.2018.1536206 |
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