Generalized Reynolds Operators on Hom-Lie Triple Systems

Abstract

Uchino first initiated the study of generalized Reynolds operators on associative algebras.
 Recently, related research has become a hot topic. In this paper, we first introduce the notion of generalized Reynolds operators on Hom-Lie triple systems associated to a representation and a 3-cocycle.
 Then, we develop cohomology of generalized Reynolds operators on Hom-Lie triple systems with coefficients in a suitable representation. As applications, we use the first cohomology group to classify linear deformations and we study the obstruction class of an extendable
 order $n$ deformation. Finally, we introduce and investigate Hom-NS-Lie triple system as the underlying
 structure of generalized Reynolds operators on Hom-Lie triple systems.