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- W2800963994 abstract "Rota--Baxter operators $R$ of weight $1$ on $mathfrak{n}$ are in bijective correspondence to post-Lie algebra structures on pairs $(mathfrak{g},mathfrak{n})$, where $mathfrak{n}$ is complete. We use such Rota--Baxter operators to study the existence and classification of post-Lie algebra structures on pairs of Lie algebras $(mathfrak{g},mathfrak{n})$, where $mathfrak{n}$ is semisimple. We show that for semisimple $mathfrak{g}$ and $mathfrak{n}$, with $mathfrak{g}$ or $mathfrak{n}$ simple, the existence of a post-Lie algebra structure on such a pair $(mathfrak{g},mathfrak{n})$ implies that $mathfrak{g}$ and $mathfrak{n}$ are isomorphic, and hence both simple. If $mathfrak{n}$ is semisimple, but $mathfrak{g}$ is not, it becomes much harder to classify post-Lie algebra structures on $(mathfrak{g},mathfrak{n})$, or even to determine the Lie algebras $mathfrak{g}$ which can arise. Here only the case $mathfrak{n}=mathfrak{sl}_2(Bbb{C})$ was studied. In this paper we determine all Lie algebras $mathfrak{g}$ such that there exists a post-Lie algebra structure on $(mathfrak{g},mathfrak{n})$ with $mathfrak{n}=mathfrak{sl}_2(Bbb{C})oplus mathfrak{sl}_2(Bbb{C})$." @default.
- W2800963994 created "2018-05-17" @default.
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- W2800963994 date "2018-05-14" @default.
- W2800963994 modified "2023-09-27" @default.
- W2800963994 title "Rota--Baxter operators and post-Lie algebra structures on semisimple Lie algebras" @default.
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