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

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.

23 pages

References in corpus (13)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Hom-algebras and homology
• Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
• Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras
• Ternary Virasoro - Witt Algebra
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• Hom-quantum groups III: Representations and module Hom-algebras
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
• Enveloping algebras of Hom-Lie algebras
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras

Cited by in corpus (22)

• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
• Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
• Cohomology and 1-parameter formal deformations of Hom-Lie triple systems
• Some constructions of multiplicative $n$-ary Hom-Nambu algebras
• A twisted generalization of Lie-Yamaguti algebras
• One-parameter formal deformations of Hom-Lie-Yamaguti algebras
• Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras
• A Hom-associative analogue of n-ary Hom-Nambu algebras
• On n-ary Hom-Nambu and Hom-Maltsev algebras
• Generalized Derivations and Rota-Baxter Operators of $n$-ary Hom-Nambu Superalgebras
• Hom-power associative algebras
• Hom-algebras via PROPs
• Quadratic $n$-ary Hom-Nambu algebras
• On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras
• On Hom-Lie antialgebra
• Hom-Lie triple system and Hom-Bol algebra structures on Hom-Malcev and right Hom-alternative algebras
• Non-Commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras
• On $(n+1)$-Hom-Lie Algebras Induced by $n$-Hom-Lie Algebras
• Double derivations of $n-$Hom-Lie color algebras
• Weighted $\mathcal{O}$-operators on Hom-Lie triple systems
• The construction of 3-Bihom-Lie algebras