Quadratic $n$-ary Hom-Nambu algebras

Abstract

The purpose of this paper is to introduce and study quadratic $n$-ary Hom-Nambu algebras, which are $n$-ary Hom-Nambu algebras with an invariant, nondegenerate and symmetric bilinear forms that are also $\alpha$-symmetric and $\beta$-invariant where $\alpha$ and $\beta$ are twisting maps. We provide constructions of these $n$-ary algebras by using twisting principles, tensor product and T*-extension. Also is discussed their connections with representation theory and centroids. Moreover we show that one may derive from quadratic $n$-ary Hom-Nambu algebra ones of increasingly higher arities and that under suitable assumptions it reduces to a quadratic $(n-1)$-ary Hom-Nambu algebra.

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Cited by in corpus (3)

• Representations and module-extensions of hom 3-Lie algebras
• Quadratic color Hom-Lie algebras
• Color Hom-Akivis algebras, Color Hom-Leibniz algebras and Modules over Color Hom-Leibniz algebras