Cohomologies of modified $\lambda$-differential Lie triple systems and applications

TL;DR

This paper introduces a new cohomology theory for modified λ-differential Lie triple systems, exploring their deformations and extensions, which advances understanding of their algebraic structure and applications.

Contribution

It develops the cohomology framework for modified λ-differential Lie triple systems and applies it to study their deformations and extensions.

Findings

Established the cohomology theory for these systems

Analyzed formal deformations of the systems

Investigated abelian extensions

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.