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

TL;DR

This paper introduces relative Rota-Baxter operators of nonzero weight on Lie triple systems, develops their cohomology theory, and uses it to classify infinitesimal deformations, advancing the understanding of their algebraic structure.

Contribution

It defines a new class of operators on Lie triple systems, establishes their cohomology, and applies it to deformation classification, providing novel insights into their structure.

Findings

Defined relative Rota-Baxter operators of weight λ on Lie triple systems.

Developed a cohomology theory for these operators.

Classified infinitesimal deformations using the first cohomology group.

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.