On n-ary Hom–Nambu and Hom–Nambu–Lie algebras

2010/04/12 by Donald Yau
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math-ph #math.MP #math.RA #msc:17A40 #msc:17A42 #msc:17C50 #msc:17D05 #msc:17D10

paper · pdf · doi:10.1016/j.geomphys.2011.11.006

published as Journal of Geometry and Physics 62 (2012) 506-522 · 23 pages

arxiv created 2010/04/12 · openalex publication_date 2011/11/21 · arxiv updated 2011/12/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02

Abstract

It is observed that the category of n-ary Hom-Nambu(-Lie) algebras is closed under twisting by self-weak morphisms. Constructions of ternary Hom-Nambu algebras from Hom-associative algebras, Hom-Lie algebras, ternary totally Hom-associative algebras, and Hom-Jordan triple systems are given. Every multiplicative n-ary Hom-Nambu algebra gives rise to a sequence of Hom-Nambu algebras of exponentially higher arities. Under some conditions, an n-ary Hom-Nambu(-Lie) algebra gives rise to an (n-1)-ary Hom-Nambu(-Lie) algebra.

Citations

• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-bialgebras and comodule Hom-algebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• Gauge symmetry and supersymmetry of multiple M2-branes
• The octonions