Cohomology and formal deformations of $n$-Hom–Lie color algebras

K. Abdaoui; R. Gharbi; S. Mabrouk; A. Makhlouf

doi:10.3842/umzh.v75i9.7238

K. Abdaoui University of Sfax, Faculty of Sciences Sfax, Tunisia
R. Gharbi University of Sfax, Faculty of Sciences Sfax, Tunisia, Université de Haute Alsace, IRIMAS – Département de Mathématiques, Mulhouse, France
S. Mabrouk University of Gafsa, Faculty of Sciences Gafsa, Tunisia
A. Makhlouf Université de Haute Alsace, IRIMAS – Département de Mathématiques, Mulhouse, France

DOI: https://doi.org/10.3842/umzh.v75i9.7238

Keywords: n-Hom-Lie color algebra

Abstract

UDC 512.5

The aim of this paper is to provide a cohomology of $n$-Hom–Lie color algebras, in particular, a cohomology governing one-parameter formal deformations. Then we also study formal deformations of the $n$-Hom–Lie color algebras and introduce the notion of Nijenhuis operator on a $n$-Hom–Lie color algebra, which may give rise to infinitesimally trivial $(n-1)$-order deformations. Furthermore, in connection with Nijenhuis operators, we introduce and discuss the notion of product structure on $n$-Hom–Lie color algebras.

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