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arXiv · 1904.01005

The infinite dimensional Unital 3-Lie Poisson algebra

Chuangchuang Kang·Ruipu Bai·Yingli Wu
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Abstract

From a commutative associative algebra $A$, the infinite dimensional unital 3-Lie Poisson algebra~$\mathfrak{L}$~is constructed, which is also a canonical Nambu 3-Lie algebra, and the structure of $\mathfrak{L}$ is discussed. It is proved that: (1) there is a minimal set of generators $S$ consisting of six vectors; (2) the quotient algebra $\mathfrak{L}/\mathbb{F}L_{0, 0}^0$ is a simple 3-Lie Poisson algebra; (3) four important infinite dimensional 3-Lie algebras: 3-Virasoro-Witt algebra $\mathcal{W}_3$, $A_\omega^\delta$, $A_{\omega}$ and the 3-$W_{\infty}$ algebra can be embedded in $\mathfrak{L}$.

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Chuangchuang Kang, Ruipu Bai, Yingli Wu. 2019-03-31. The infinite dimensional Unital 3-Lie Poisson algebra. https://arxiv.org/abs/1904.01005

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