On Nijenhuis Lie triple systems

Abstract: In this paper, we investigate the mathematical structure of Nijenhuis Lie triple systems, an extension of classical Lie triple systems augmented with the Nijenhuis operator. Our study focuses on the cohomology of Nijenhuis Lie triple systems and demonstrates how abelian extensions of Nijenhuis Lie triple systems are related to cohomology groups. Additionally, we define Nijenhuis Lie triple 2-systems and also classify strict' andskeletal' Nijenhuis Lie triple 2-systems in terms of crossed modules and the cohomology of Nijenhuis Lie triple systems.