Reynolds operators on Hom-Leibniz algebras

Abstract

In this paper, we first  introduce the notion of  Reynolds operators on  Hom-Leibniz algebras and give some constructions.   Furthermore,   we define the cohomology of  Reynolds operators,  and use this cohomology to study deformations of Reynolds operators.   As applications,  we introduce and study NS-Hom-Leibniz algebras as the underlying structure of Reynolds operators.