{"paper":{"title":"The infinite dimensional Unital 3-Lie Poisson algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RA","authors_text":"Chuangchuang Kang, Ruipu Bai, Yingli Wu","submitted_at":"2019-03-31T21:05:20Z","abstract_excerpt":"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 $\\mathfr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01005","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}