Wells exact sequence for automorphisms and derivations of Leibniz 2-algebras

TL;DR

This paper extends the Wells exact sequence framework to Leibniz 2-algebras, analyzing automorphisms and derivations, and explores their inducibility and cohomological properties, including special cases like crossed modules.

Contribution

It introduces the Wells exact sequence analog for Leibniz 2-algebras and studies automorphisms and derivations within this new context.

Findings

Established Wells exact sequence for Leibniz 2-algebras

Analyzed inducibility of automorphisms and derivations

Explored special cases like crossed modules

Abstract

In this paper, we investigate the inducibility of pairs of automorphisms and derivations in Leibniz 2-algebras. To begin, we provide essential background information on Leibniz 2-algebras and its cohomology theory. Next, we examine the inducibility of pairs of automorphisms and derivations, with a focus on the analog of Wells exact sequences in the context of Leibniz 2-algebras. We then analyze the analogue of Wells short exact sequences as they relate to automorphisms and derivations within this framework. Finally, we investigate the special case of crossed modules over Leibniz algebras.