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arXiv · 2401.02593

Classification of Transposed Poisson 3-Lie algebras of dimension 3

Jiang Yaxi·Kang Chuangchuang·Lü Jiafeng
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Abstract

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 $\mathbb{C}$.

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Jiang Yaxi, Kang Chuangchuang, Lü Jiafeng. 2024-01-05. Classification of Transposed Poisson 3-Lie algebras of dimension 3. https://arxiv.org/abs/2401.02593

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