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

TL;DR

This paper explores the structure and construction methods of n-ary Hom-Nambu and Hom-Nambu-Lie algebras, demonstrating their closure properties and how they can be derived from various algebraic systems.

Contribution

It introduces new constructions of n-ary Hom-Nambu algebras from existing algebraic frameworks and shows how these algebras can generate higher or lower arity algebras.

Findings

Category of n-ary Hom-Nambu algebras is closed under twisting.

Constructs of ternary Hom-Nambu algebras from various algebraic systems are provided.

Multiplicative n-ary Hom-Nambu algebras generate higher arity 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.