Cohomologies of modified λ-differential Lie triple systems and applications

Abstract

In this paper, we introduce the concept and representation of modified $ \lambda $-differential Lie triple systems. Next, we define the cohomology of modified $ \lambda $-differential Lie triple systems with coefficients in a suitable representation. As applications of the proposed cohomology theory, we study 1-parameter formal deformations and abelian extensions of modified $ \lambda $-differential Lie triple systems.

Keywords

• lie triple system
• modified $ \lambda $-differential operator
• cohomology
• deformation
• extension