Classification of Transposed Poisson 3-Lie algebras of dimension 3
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912217527484416 |
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| author | Yaxi, Jiang Chuangchuang, Kang Jiafeng, Lü |
| author_facet | Yaxi, Jiang Chuangchuang, Kang Jiafeng, Lü |
| contents | Transposed Poisson $3$-Lie algebra is a dual notion of Nambu-Poisson algebra of order 3. In this paper, we explicitly determine all $\frac{1}{3}$-derivations and automorphisms of the unique nontrivial $3$-dimensional complex $3$-Lie algebra $(A_3,[\cdot,\cdot,\cdot])$. Based on the one-one correspondence between $\frac{1}{3}$-derivations and transposed Poisson 3-Lie algebras, up to isomorphism, we classify transposed Poisson $3$-Lie algebras of dimension $3$ under the case that $L_{e_1}$ is trivial over the complex field $\mathbb{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of Transposed Poisson 3-Lie algebras of dimension 3 Yaxi, Jiang Chuangchuang, Kang Jiafeng, Lü Rings and Algebras Mathematical Physics 17A36, 17A30, 17A40, 17A42, 17B63 Transposed Poisson $3$-Lie algebra is a dual notion of Nambu-Poisson algebra of order 3. In this paper, we explicitly determine all $\frac{1}{3}$-derivations and automorphisms of the unique nontrivial $3$-dimensional complex $3$-Lie algebra $(A_3,[\cdot,\cdot,\cdot])$. Based on the one-one correspondence between $\frac{1}{3}$-derivations and transposed Poisson 3-Lie algebras, up to isomorphism, we classify transposed Poisson $3$-Lie algebras of dimension $3$ under the case that $L_{e_1}$ is trivial over the complex field $\mathbb{C}$. |
| title | Classification of Transposed Poisson 3-Lie algebras of dimension 3 |
| topic | Rings and Algebras Mathematical Physics 17A36, 17A30, 17A40, 17A42, 17B63 |
| url | https://arxiv.org/abs/2401.02593 |