Generalized Reynolds Operators on Hom-Lie Triple Systems

Abstract

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 a cohomology of generalized Reynolds operators on Hom-Lie triple systems. 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.

Keywords

• Hom-Lie triple system
• generalized Reynolds operator
• cohomology
• deformation
• Hom-NS-Lie triple system