On n-Hom-pre-Lie Color algebras and associated Kupershmidt operators

Abstract

In this paper, we introduce the Hom-color generalization of n-pre-Lie algebras called n-Hom-pre-Lie color algebras in which, we investigate their representation theory and we give some related results and structures based on Rota-Baxter operators, Kupershmidt operators and Nijenhuis operators. Moreover, we show that given (n−2)-linear form of a Hom-pre-Lie color algebra satisfying certain conditions, one can construct a structure of n-Hom-pre-Lie
color algebra called induced n-Hom-pre-Lie color ralgebra. The same procedure is applied for the representation of n-Hom-pre-Lie color algebras.