Author(s): F AMMAR, S MABROUK, A MAKHLOUF
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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 α-symmetric and β-invariant where α and β 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.
This article was published in arXiv.org
and referenced in Journal of Generalized Lie Theory and Applications