Modified Rota-Baxter Lie triple systems with higher derivations

Abstract

In this paper, we consider modified Rota-Baxter Lie triple systems with higher derivations. A pair consisting of a modified Rota-Baxter Lie triple system and a higher derivation is called a modified Rota-Baxter LieTHDer pair. We
investigate cohomologies of a modified Rota-Baxter LieTHDer pairs with coefficients in a suitable representation. As applications, we study abelian extensions and formal one-parameter deformations of modified
Rota-Baxter LieTHDer pairs.