Some constructions of multiplicative $n$-ary Hom-Nambu algebras
Abdelkader Ben Hassine, Sami Mabrouk, Othmen Ncib

TL;DR
This paper presents methods to construct multiplicative n-ary Hom-Nambu algebras from Hom-Lie algebras, establishing conditions for their algebraic identities and introducing a generalized Hom-Lie n-uplet system.
Contribution
It introduces new constructions of n-Hom-Lie algebras from Hom-Lie algebras and defines the Hom-Lie n-uplet system as a generalization of Hom-Lie triple systems.
Findings
Constructed n-ary Hom-Lie brackets from Hom-Lie algebras.
Identified conditions for the Filippov-Jacobi identity in these constructions.
Introduced the Hom-Lie n-uplet system as a generalization.
Abstract
We show that given a Hom-Lie algebra one can construct the n-ary Hom-Lie bracket by means of an (n-2)-cochain of given Hom-Lie algebra and find the conditions under which this n-ary bracket satisfies the Filippov-Jacobi identity, there by inducing the structure of n-Hom-Lie algebra. We introduce the notion of Hom-Lie -uplet system which is the generalization of Hom-Lie triple system. We construct Hom-Lie -uplet system using a Hom-Lie algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Rings, Modules, and Algebras
