Non-abelian extensions and Wells exact sequences of Bol algebras

TL;DR

This paper investigates non-abelian extensions of Bol algebras, classifies them via cohomology, and derives Wells exact sequences to understand automorphism extensibility within these structures.

Contribution

It introduces a classification of non-abelian Bol algebra extensions using cohomology and establishes Wells exact sequences for automorphism extension analysis.

Findings

Classification of non-abelian extensions via cohomology groups

Conditions for automorphism extension in non-abelian extensions

Derivation of Wells exact sequences for Bol algebras

Abstract

The aim of this paper is to explore non-abelian extensions of Bol algebras and to study the extensibility of a pair of automorphisms within these non-abelian extensions. We begin by researching non-abelian extensions of Bol algebras and categorizing them based on non-abelian cohomology groups. Additionally, we discuss the conditions under which a pair of automorphisms can be extended in the context of non-abelian extensions of Bol algebras and derive the corresponding Wells exact sequences.