Central extensions of precrossed modules
type: Item
instance of: scholarly article
title: Central extensions of precrossed modules
zbMATH Open document ID: 1087.18010
DOI: 10.1023/B:APCS.0000040555.48968.64
author: Daniel Arias
author: M. Ladra
published in: Applied Categorical Structures
publication date: 2005-01-17T00:00:00Z
review text: The cohomology of crossed modules studied by \textit{P. Carrasco, A. M. Cegarra} and \textit{A. R. Grandjeán} [J. Pure Appl. Algebra 168, 147--176 (2002; Zbl 0996.18010)] allowed the classification of crossed module central extensions. In this paper this result is extended to the category of precrossed modules (that is, crossed modules where Peiffer's condition does not hold). The authors prove that the second cohomology group of precrossed modules classifies the precrossed module central extensions. Then, a description of these central extensions is given by using a universal coefficient theorem for the (co)homology of precrossed modules that is also established in the paper.
reviewed by: Antonio R. Garzón
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 2128568
zbMATH Keywords: central extension
zbMATH Keywords: precrossed module
zbMATH Keywords: cohomology
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2128568