On non-abelian extensions of 3-Lie algebras

TL;DR

This paper explores the classification of non-abelian extensions of 3-Lie algebras using Maurer-Cartan elements, establishing a correspondence with their equivalence classes and analyzing related Leibniz algebra structures.

Contribution

It introduces a novel approach linking non-abelian extensions of 3-Lie algebras to Maurer-Cartan elements in a DGLA, providing a new classification framework.

Findings

One-to-one correspondence between extensions and Maurer-Cartan classes

Characterization of Leibniz algebra structures on fundamental objects

Framework for classifying non-abelian 3-Lie algebra extensions

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.