Higher central extensions and Hopf formulae

TL;DR

This paper explores higher central extensions in non-abelian homological algebra, establishing their fundamental properties and proving the invariance of higher Hopf formulae.

Contribution

It provides a direct proof of the invariance of higher Hopf formulae and advances understanding of higher central extensions.

Findings

Proved fundamental properties of higher central extensions

Established invariance of higher Hopf formulae

Enhanced theoretical framework for non-abelian homological algebra

Abstract

Higher extensions and higher central extensions, which are of importance to non-abelian homological algebra, are studied, and some fundamental properties are proven. As an application, a direct proof of the invariance of the higher Hopf formulae is obtained.