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

It is observed that the category of n-ary Horn-Nambu(-Lie) algebras is closed under twisting by self-weak morphisms. Constructions of ternary Hom-Nambu algebras from Horn-associative algebras, Horn-Lie algebras, ternary totally Horn-associative algebras, and Horn-Jordan triple systems are given. Every multiplicative n-ary Horn-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. (C) 2011 Elsevier B.V. All rights reserved.