Cohomology, Extensions and Deformations of restricted Lie triple systems

The main purpose of this paper is to provide a cohomology theory of restricted Lie triple systems in low degrees and their algebraic interpretations. We define restricted cochains up to degree 5, together with the corresponding coboundary operators. Moreover, we provide interpretations of the low-degree restricted cohomology groups in terms of restricted derivations, extensions of restricted modules, formal deformations, and extensions of restricted Lie triple systems.