Non-abelian Extensions of Lie 2-algebras

TL;DR

This paper introduces derivations of Lie 2-algebras and classifies their non-abelian extensions using morphisms to a derivation Lie 3-algebra, advancing the understanding of higher Lie algebra structures.

Contribution

It defines derivations for Lie 2-algebras, constructs a derivation Lie 3-algebra, and classifies non-abelian extensions via morphisms to this algebra.

Findings

Derivations of Lie 2-algebras are formally introduced.

A derivation Lie 3-algebra is constructed.

Non-abelian extensions are classified by morphisms to the derivation Lie 3-algebra.

Abstract

In this paper, we introduce the notion of derivations of Lie 2-algebras and construct the associated derivation Lie 3-algebra. We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie 3-algebra.