On non-abelian extensions of 3-Lie algebras

Abstract

In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed.

17 pages

References in corpus (5)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• n-ary algebras: a review with applications
• M2-branes, 3-Lie Algebras and Plucker relations
• Hydrodynamic Limit For An Active Exclusion Process
• A new approach to representations of $3$-Lie algebras and abelian extensions

Cited by in corpus (3)

• Review of deformation theory I: Concrete formulas for deformations of algebraic structures
• Nonabelian embedding tensors
• Generalized representations of 3-Hom-Lie algebras