Twisting of Lie triple systems, $L_\infty$-algebras, and (generalized) matched pairs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910488975114240 |
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| author | Zhao, Jia Xia, Haobo |
| author_facet | Zhao, Jia Xia, Haobo |
| contents | In this paper, we introduce notions of (proto-, quasi-)twilled Lie triple systems and give their equivalent descriptions using the controlling algebra and bidegree convention. Then we construct an $L_\infty$-algebra via a twilled Lie triple system. Besides, we establish the twisting theory of Lie triple systems and then characterize the twisting as a Maurer-Cartan element in the constructed $L_\infty$-algebra. Finally, we clarify the relationship between twilled Lie triple systems and matched pairs and clarify the relationship between twilled Lie triple systems and relative Rota-Baxter operators respectively so that we obtain the relationship between matched pairs of Lie triple systems and relative Rota-Baxter operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisting of Lie triple systems, $L_\infty$-algebras, and (generalized) matched pairs Zhao, Jia Xia, Haobo Rings and Algebras In this paper, we introduce notions of (proto-, quasi-)twilled Lie triple systems and give their equivalent descriptions using the controlling algebra and bidegree convention. Then we construct an $L_\infty$-algebra via a twilled Lie triple system. Besides, we establish the twisting theory of Lie triple systems and then characterize the twisting as a Maurer-Cartan element in the constructed $L_\infty$-algebra. Finally, we clarify the relationship between twilled Lie triple systems and matched pairs and clarify the relationship between twilled Lie triple systems and relative Rota-Baxter operators respectively so that we obtain the relationship between matched pairs of Lie triple systems and relative Rota-Baxter operators. |
| title | Twisting of Lie triple systems, $L_\infty$-algebras, and (generalized) matched pairs |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2406.10596 |