Cohomology for Deformation maps on quasi-twilled Lie triple systems

Due to the importance of invariant, in the present paper, we provide a unified approach to study various kinds of operators on Lie triple systems such as crossed homomorphisms, relative Rota-Baxter operators, Reynolds operators etc.

For this purpose, we examine two kinds of deformation maps on quasi-twilled Lie triple systems.

A quasi-twilled Lie triple system is a Lie triple system which can be decomposed into two subspaces, one of which is a subalgebra.

Moreover, we establish cohomologies of two kinds of deformation maps, which recover those of several kinds of operators on Lie triple systems.