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.
Categories: math.RT math-ph math.MP