The chain complex of an acyclic simplicial \(G\)-complex
type: Item
instance of: scholarly article
title: The chain complex of an acyclic simplicial \(G\)-complex
zbMATH Open document ID: 0940.55020
author: Serge Bouc
published in: Journal of Algebra
publication date: 2000-02-01T00:00:00Z
review text: For a finite group \(G\), the reduced chain complex of an acyclic finite-dimensional simplicial \(G\)-complex is a split acyclic complex of \(\mathbb{Z} G\)-modules. The main tool of this result is the notion of a permutation module (i.e. having a stable basis). A key theorem says that some complexes of permutation modules are split acyclic iff all of their Brauer quotients are acyclic.
Mathematics Subject Classification ID: 55U15
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 18G35
zbMATH DE Number: 1384466
zbMATH Keywords: acyclic simplicial complex
zbMATH Keywords: Brauer quotient
zbMATH Keywords: simplicial \(G\)-complex
zbMATH Keywords: permutation module
reviewed by: Georges Hoff
MaRDI profile type: Publication
full work available at URL: jabr.1999.7983
OpenAlex ID: W1996611439
cites work: Q4023148
cites work: Q4378346
cites work: Q5509718
DOI: 10.1006/JABR.1999.7983
description: scientific article; zbMATH DE number 1384466