Integration of derivations for Lie $2$-algebras

TL;DR

This paper constructs the automorphism 2-group of a Lie 2-algebra, demonstrating it as an integration of the derivation Lie 2-algebra, thus advancing the understanding of higher algebraic structures.

Contribution

It introduces a method to integrate derivations of Lie 2-algebras into their automorphism 2-groups, providing a new perspective on higher algebraic symmetries.

Findings

Automorphism 2-group $ ext{Aut}( ext{g})$ constructed for Lie 2-algebras

$ ext{Aut}( ext{g})$ shown to be an integration of $ ext{Der}( ext{g})$

Establishes a link between derivations and automorphisms in higher algebra

Abstract

In this paper, for a Lie 2-algebra $\g$, we construct the automorphism 2-group $\Aut(\g)$, which turns out to be an integration of the derivation Lie 2-algebra $\Der(\g)$.