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.

arXiv comment17 pages

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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