Deformations and extensions of modified $\lambda$-differential $3$-Lie Algebras

TL;DR

This paper develops a cohomology theory for modified λ-differential 3-Lie algebras and explores their deformations and extensions, providing new tools for understanding their structure and classifications.

Contribution

It introduces a cohomology framework for modified λ-differential 3-Lie algebras and applies it to study their deformations and extensions, which is a novel approach.

Findings

Defined the cohomology of modified λ-differential 3-Lie algebras.

Analyzed linear deformations and abelian extensions.

Explored T*-extensions of these algebras.

Abstract

In this paper, we introduce the representation of modified $\lambda$-differential $3$-Lie algebras and define the cohomology of modified $\lambda$-differential $3$-Lie algebras with coefficients in a representation. As applications of the proposed cohomology theory, we study linear deformations, abelian extensions and $T^*$-extensions of modified $\lambda$-differential $3$-Lie algebras.