Non-abelian extensions of Lie triple systems and Wells exact sequences

TL;DR

This paper studies the structure and classification of non-abelian extensions of Lie triple systems, introduces cohomology-based classification methods, and derives Wells exact sequences for automorphism pairs.

Contribution

It develops a cohomology framework for non-abelian extensions and extends Wells exact sequences to Lie triple systems.

Findings

Classified non-abelian extensions via cohomology groups

Characterized extensions using Maurer-Cartan elements

Derived Wells exact sequences for automorphism pairs

Abstract

In this paper, we investigate non-abelian extensions and inducibility of pairs of automorphisms of Lie triple systems. First, we introduce non-abelian cohomology groups and classify the non-abelian extensions in terms of non-abelian cohomology groups. Next, we characterize the non-abelian extensions using Maurer-Cartan elements. Furthermore, we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Lie triple systems. Finally, we state the previous results under the context of abelian extensions of Lie triple systems.