Deformations and Extensions of Modified λ-Differential 3-Lie Algebras

Abstract

In this paper, we propose the representation and cohomology of modified λ-differential 3-Lie algebras. As their applications, the linear deformations, abelian extensions and T∗-extensions of modified λ-differential 3-Lie algebras are also studied.

Abelian Extensions of Modified λ-Differential Left-Symmetric Algebras and Crossed Modules

“…Inspired from [9,10], the notion of modified λ-differential Lie algebras was introduced in [11]. Subsequently, the algebraic structures with modified operators were widely studied in [12][13][14][15][16].…”

“…Motivated by the work in [8,[11][12][13], our main purpose is to study the representation and cohomology of the modified λ-differential left symmetric algebras and applied them to the linear deformation, abelian extension, and skeletal modified λ-differential left symmetric 2-algebras. The paper is organized as follows.…”

Abelian Extensions and Crossed Modules of Modified λ-Differential Left-Symmetric Algebras

“…Motivated by the modified r-matrices, in [11], Peng and his collaborators introduced the concept of modified λ-differential Lie algebras. Subsequently, the algebraic structures with modified operators have been widely studied in [12][13][14][15][16][17][18].…”