Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911832229281792 |
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| author | Goncharov, Maxim |
| author_facet | Goncharov, Maxim |
| contents | In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a motivation, we show that there is a natural connection between Rota-Baxter operators of this type and structures of quasitriangular Lie bialgebras on a quadratic finite-dimensional Lie algebra. Moreover, we show that some classical results on Lie bialgebra structure on simple finite-dimensional Lie algebras can be obtained from the corresponding results for Rota-Baxter operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13697 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures Goncharov, Maxim Rings and Algebras 17B38, 17B62 In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a motivation, we show that there is a natural connection between Rota-Baxter operators of this type and structures of quasitriangular Lie bialgebras on a quadratic finite-dimensional Lie algebra. Moreover, we show that some classical results on Lie bialgebra structure on simple finite-dimensional Lie algebras can be obtained from the corresponding results for Rota-Baxter operators. |
| title | Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures |
| topic | Rings and Algebras 17B38, 17B62 |
| url | https://arxiv.org/abs/2403.13697 |