Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909707567890432 |
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| author | Li, Haiying Ma, Tianshui |
| author_facet | Li, Haiying Ma, Tianshui |
| contents | In this paper the conditions that when a Lie algebra is Nijenhuis are investigated. Furthermore all the Nijenhuis operators on $\mathfrak{sl}_2$ under the standard Cartan-Weyl basis are given. On the other hand, the relations between the classical Yang-Baxter equation and Nijenhuis operators $N$ on a Lie algebra and $P$ on a Lie coalgebra are derived by means of the bialgebraic theory for Nijenhuis Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras Li, Haiying Ma, Tianshui Rings and Algebras In this paper the conditions that when a Lie algebra is Nijenhuis are investigated. Furthermore all the Nijenhuis operators on $\mathfrak{sl}_2$ under the standard Cartan-Weyl basis are given. On the other hand, the relations between the classical Yang-Baxter equation and Nijenhuis operators $N$ on a Lie algebra and $P$ on a Lie coalgebra are derived by means of the bialgebraic theory for Nijenhuis Lie algebras. |
| title | Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2502.18717 |