Universal central extensions of precrossed modules and Milnor's relative \(K_{2}\)
type: Item
instance of: scholarly article
title: Universal central extensions of precrossed modules and Milnor's relative \(K_{2}\)
zbMATH Open document ID: 1027.19002
DOI: 10.1016/S0022-4049(03)00065-3
author: M. Ladra
author: Daniel Arias
author: A. R. Grandjeán
published in: Journal of Pure and Applied Algebra
publication date: 2003-10-15T00:00:00Z
review text: A precrossed module \((M,P,\mu)\) is a group homomorphism \(\mu:M\to P\) together with an action of \(P\) on \(M\) satisfying \(\mu({}^pm)=p\mu(m)p^{-1}\). If one also has \({}^{\mu(m)}m'=mm'm^{-1}\) for \(m,m'\in M\), then it is a crossed module. The authors define universal central extensions of perfect precrossed modules. They also have a five term exact sequence in homology and an analogue of Hopf's formula for the second homology group. However, precrossed modules are not what is needed to get the relative Steinberg group of Keune and Loday. For that one needs to use crossed modules.
reviewed by: Wilberd van der Kallen
Mathematics Subject Classification ID: 19C09
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 19M05
zbMATH DE Number: 1993279
zbMATH Keywords: precrossed module
zbMATH Keywords: universal central extension
zbMATH Keywords: Hopf formula
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1993279