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

Abstract

Hom-alternative and Hom-Jordan algebras are shown to give rise to Hom-Nambu algebras of arities 2^{k+1} + 1. The class of n-ary Hom-Maltsev algebras is studied. Multiplicative n-ary Hom-Nambu-Lie algebras are shown to be n-ary Hom-Maltsev algebras. Examples of ternary Hom-Maltsev algebras that are not ternary Hom-Nambu-Lie algebras are given. Ternary Hom-Maltsev algebras are shown to arise from composition algebras.

24 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
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• 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
• Hom-alternative algebras and Hom-Jordan algebras
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras

Cited by in corpus (7)

• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• A Hom-associative analogue of n-ary Hom-Nambu 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
• Hom-Lie triple system and Hom-Bol algebra structures on Hom-Malcev and right Hom-alternative algebras