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.
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Xiao et al. (2024) studied this question.
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