Cohomology and Formal Deformations of n-Hom–Lie Color Algebras

We provide a cohomology of n -Hom–Lie color algebras, in particular, a cohomology governing oneparameter formal deformations. Then we also study formal deformations of the n -Hom–Lie color algebras and introduce the notion of Nijenhuis operator on an n -Hom–Lie color algebra, which may give rise to infinitesimally trivial ( n − 1)th-order deformations. Furthermore, in connection with Nijenhuis operators, we introduce and discuss the notion of product structure on n -Hom–Lie color algebras.