Rota-Baxter operators on compact simple Lie groups and algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916796795191296 |
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| author | Skresanov, Saveliy V. |
| author_facet | Skresanov, Saveliy V. |
| contents | A Rota-Baxter operator on a Lie group $ G $ is a smooth map $ B : G \to G $ such that $ B(g)B(h) = B(gB(g)hB(g)^{-1}) $ for all $ g, h \in G $. This concept was introduced in 2021 by Guo, Lang and Sheng as a Lie group analogue of Rota-Baxter operators of weight 1 on Lie algebras. We show that the only Rota-Baxter operators on compact simple Lie groups are the trivial map and the inverse map. A similar description for Rota-Baxter operators of weight 1 on compact simple Lie algebras is provided. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_14324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rota-Baxter operators on compact simple Lie groups and algebras Skresanov, Saveliy V. Group Theory Rings and Algebras 22E60 (Primary) 17B38 (Secondary) A Rota-Baxter operator on a Lie group $ G $ is a smooth map $ B : G \to G $ such that $ B(g)B(h) = B(gB(g)hB(g)^{-1}) $ for all $ g, h \in G $. This concept was introduced in 2021 by Guo, Lang and Sheng as a Lie group analogue of Rota-Baxter operators of weight 1 on Lie algebras. We show that the only Rota-Baxter operators on compact simple Lie groups are the trivial map and the inverse map. A similar description for Rota-Baxter operators of weight 1 on compact simple Lie algebras is provided. |
| title | Rota-Baxter operators on compact simple Lie groups and algebras |
| topic | Group Theory Rings and Algebras 22E60 (Primary) 17B38 (Secondary) |
| url | https://arxiv.org/abs/2506.14324 |