Quadratic $n$-ary Hom-Nambu algebras

Details Quadratic $n$-ary Hom-Nambu algebras Quadratic $n$-ary Hom-Nambu algebras

2011-10-10

arxiv.org/abs/1110.2078v1

Mathematics

Rings and Algebras

Scientific paper

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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