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

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.

33pages,a primary edition. arXiv admin note: text overlap with arXiv:2310.07719; text overlap with arXiv:1508.01850 by other authors