The infinite dimensional Unital 3-Lie Poisson algebra

2019/03/31 by Chuangchuang Kang, Kang, Chuangchuang, Ruipu Bai +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1904.01005

openalex publication_date 2019/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

From a commutative associative algebra A, the infinite dimensional unital 3-Lie Poisson algebra~\mathfrakL~is constructed, which is also a canonical Nambu 3-Lie algebra, and the structure of \mathfrakL is discussed. It is proved that: (1) there is a minimal set of generators S consisting of six vectors; (2) the quotient algebra \mathfrakL/\mathbbFL_{0, 0}⁰ is a simple 3-Lie Poisson algebra; (3) four important infinite dimensional 3-Lie algebras: 3-Virasoro-Witt algebra W₃, A_ω^δ, A_ω and the 3-W_∞ algebra can be embedded in \mathfrakL.

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