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arXiv · 1809.01067

Some constructions of multiplicative $n$-ary Hom-Nambu algebras

Abdelkader Ben Hassine·Sami Mabrouk·Othmen Ncib
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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 $n$-uplet system which is the generalization of Hom-Lie triple system. We construct Hom-Lie $n$-uplet system using a Hom-Lie algebra.

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Abdelkader Ben Hassine, Sami Mabrouk, Othmen Ncib. 2018-09-04. Some constructions of multiplicative $n$-ary Hom-Nambu algebras. https://doi.org/10.1007/s00006-019-0996-6

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