The non-abelian extension and Wells map of Leibniz conformal algebra

2025/03/20 by Zhao, Jun, Hou, Bo, Zhou, Xin
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2503.15938

Abstract

In this paper, we study the theory of non-abelian extensions of a Leibniz conformal algebra R by a Leibniz conformal algebra H and prove that all the non-abelian extensions are classified by non-abelian 2nd cohomology H²_nab(R,H) in the sense of equivalence. Then we introduce a differential graded Lie algebra \mathfrakL and show that the set of its Maurer-Cartan elements in bijection with the set of non-abelian extensions. Finally, as an application of non-abelian extension, we consider the inducibility of a pair of automorphisms about a non-abelian extension, and give the fundamental sequence of Wells of Leibniz conformal algebra R. Especially, we discuss the extensibility problem of derivations about an abelian extension of R.

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