O-operators on Lie triple systems

TL;DR

This paper investigates the cohomology and deformation theory of $\\mathcal{O}$-operators on Lie triple systems, establishing their relationships with Lie algebra $\\mathcal{O}$-operators and Lie-Yamaguti cohomology.

Contribution

It introduces a cohomology framework for $\\mathcal{O}$-operators on Lie triple systems and explores their deformations and connections to Lie algebra $\\mathcal{O}$-operators.

Findings

Defined a cohomology for $\\mathcal{O}$-operators using Lie-Yamaguti cohomology.

Analyzed infinitesimal and formal deformations of $\\mathcal{O}$-operators.

Established relationships between $\\mathcal{O}$-operators on Lie algebras and Lie triple systems.

Abstract

The purpose of this paper is to study cohomology and deformations of $\mathcal{O}$-operators on Lie triple systems. We define a cohomology of an $\mathcal{O}$-operator $T$ as the Lie-Yamaguti cohomology of a certain Lie triple system induced by $T$ with coefficients in a suitable representation. Then we consider infinitesimal and formal deformations of $\mathcal{O}$-operators from cohomological viewpoint. Moreover we provide relationships between $\mathcal{O}$-operators on Lie algebras and associated Lie triple systems.