Low-dimensional (co)homology of free Burnside monoids
type: Item
instance of: scholarly article
title: Low-dimensional (co)homology of free Burnside monoids
zbMATH Open document ID: 0852.20060
DOI: 10.1016/0022-4049(95)00038-0
published in: Journal of Pure and Applied Algebra
publication date: 1996-12-10T00:00:00Z
review text: Let \(r\geq 0\), \(m,d\geq 1\) be integers and let \(M_{r,m,d}\) be the free Burnside monoid defined by the presentation \({\mathcal B}_{r,m,d}=\langle\Sigma\mid X^{m+d}=X^m\), \(X\) any word \(\rangle\), where \(\Sigma\) is a set of cardinality \(r\). In the article, the second and third integral (co)homology groups of \(M_{r,m,d}\) are calculated: it is proved that for \(r>1\), \(m\geq 3\), \(d\geq 1\), \(H_2(M_{r,m,d})\) is a free abelian group of infinite rank and that \(H_3(M_{r,m,d})\) is a direct sum of infinitely many copies of \(Z_d\).
reviewed by: Peeter Normak
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 897482
zbMATH Keywords: free Burnside monoids
zbMATH Keywords: presentations
zbMATH Keywords: integral (co)homology groups
author: Victor S. Guba
author: Stephen J. Pride
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00038-0
OpenAlex ID: W2158700102
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description: scientific article; zbMATH DE number 897482