2011/10/10 by Ammar, Faouzi, Mabrouk, Sami, Makhlouf, Abdenacer
#17A30 #17A36 #17A42 #17A45 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1110.2078
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.