Nonabelian embedding tensors on 3-Lie algebras and 3-Leibniz-Lie algebras
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908278278062080 |
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| author | Teng, Wen Dai, Xiansheng |
| author_facet | Teng, Wen Dai, Xiansheng |
| contents | In this paper, first we introduce the notion of a nonabelian embedding tensor on the 3-Lie algebra. Then, we introduce the notion of a 3-Leibniz-Lie algebra, which is the underlying algebraic structure of a nonabelian embedding tensor on the 3-Lie algebra, and can also be viewed as a nonabelian generalization of a 3-Leibniz algebra. Next we develop the cohomology of nonabelian embedding tensors on 3-Lie algebras with coefficients in a suitable representation and use the first cohomology group to characterize infinitesimal deformations. Finally, we investigate nonabelian embedding tensors on 3-Lie algebras induced by Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06990 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonabelian embedding tensors on 3-Lie algebras and 3-Leibniz-Lie algebras Teng, Wen Dai, Xiansheng Rings and Algebras 17A42, 17B56, 17B38, 17B40 In this paper, first we introduce the notion of a nonabelian embedding tensor on the 3-Lie algebra. Then, we introduce the notion of a 3-Leibniz-Lie algebra, which is the underlying algebraic structure of a nonabelian embedding tensor on the 3-Lie algebra, and can also be viewed as a nonabelian generalization of a 3-Leibniz algebra. Next we develop the cohomology of nonabelian embedding tensors on 3-Lie algebras with coefficients in a suitable representation and use the first cohomology group to characterize infinitesimal deformations. Finally, we investigate nonabelian embedding tensors on 3-Lie algebras induced by Lie algebras. |
| title | Nonabelian embedding tensors on 3-Lie algebras and 3-Leibniz-Lie algebras |
| topic | Rings and Algebras 17A42, 17B56, 17B38, 17B40 |
| url | https://arxiv.org/abs/2310.06990 |