Relative Rota-Baxter operators of nonzero weights on Lie Triple Systems

Abstract: In this paper, we introduce the notion of a relative Rota-Baxter operator of weight $\lambda$ on a Lie triple system with respect to an action on another Lie triple system, which can be characterized by the graph of their semidirect product. We also establish a cohomology theory for a relative Rota-Baxter operator of weight $\lambda$ on Lie triple systems and use the first cohomology group to classify infinitesimal deformations.