n-Lie algebras

2009/09/08 by Michel Goze, Goze, Michel, Nicolas Goze +3 · 4 citations
Mathematics · Physics and Astronomy · #17A42 #58F05 #70H05 #Advanced Differential Geometry Research #Advanced Topics in Algebra #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.0909.1419

openalex publication_date 2009/09/08 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The notion of n-ary algebras, that is vector spaces with a multiplication concerning n-arguments, n ≥ 3, became fundamental since the works of Nambu. Here we first present general notions concerning n-ary algebras and associative n-ary algebras. Then we will be interested in the notion of n-Lie algebras, initiated by Filippov, and which is attached to the Nambu algebras. We study the particular case of nilpotent or filiform n-Lie algebras to obtain a beginning of classification. This notion of n-Lie algebra admits a natural generalization in Strong Homotopy n-Lie algebras in which the Maurer Cartan calculus is well adapted.

Cited by

• Nijenhuis operators and twisted O-operators on Nambu-Poisson algebras
• Fundamental theorem of Poisson 3-Lie (A,H)-Hopf modules
• Twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras
• Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras

Related

• n-ary Lie and Associative Algebras
• Lie algebra of an n-Lie algebra
• Elementary n-Lie algebras
• On n-ary Generalization of BiHom-Lie Algebras and BiHom-Associative\n Algebras
• The Classification of n-Lie Algebras