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

TL;DR

This paper develops a cohomology theory for n-Hom-Lie color algebras, explores their formal deformations, introduces Nijenhuis operators, and discusses product structures, advancing the understanding of their algebraic properties.

Contribution

It introduces a cohomology framework for n-Hom-Lie color algebras and studies their deformations and Nijenhuis operators, which are new contributions to the field.

Findings

Cohomology governing one-parameter formal deformations is established.

Nijenhuis operators can generate infinitesimally trivial deformations.

A new notion of product structure on n-Hom-Lie color algebras is proposed.

Abstract

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