Deformations and extensions of modified $\lambda$-differential $3$-Lie 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 $T^{\ast }$-extensions of modified $\lambda$-differential $3$-Lie algebras.

References in corpus (6)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• M2-branes, 3-Lie Algebras and Plucker relations
• Multiple M2-branes and Generalized 3-Lie algebras
• $3$-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras
• Deformations and cohomology theory of Rota-Baxter $3$-Lie algebras of arbitrary weights