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

It is observed that the category of nn-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 nn-ary Hom–Nambu algebra gives rise to a sequence of Hom–Nambu algebras of exponentially higher arities. Under some conditions, an nn-ary Hom–Nambu(–Lie) algebra gives rise to an (n−1)(n−1)-ary Hom–Nambu(–Lie) algebra.