On the minimality of Anick's resolution, with application to an algebra of cohomology operations
type: Item
instance of: scholarly article
title: On the minimality of Anick's resolution, with application to an algebra of cohomology operations
zbMATH Open document ID: 0845.18008
author: William M. Singer
published in: Journal of Algebra
publication date: 1996-07-09T00:00:00Z
review text: Let \(k\) be a field, \(G\) an augmented \(k\)-algebra, generated by a set \(S\). In his paper ``Homology of associative algebras'' [Trans. Am. Math. Soc. 296, 641-659 (1986; Zbl 0598.16028)] \textit{D. J. Anick} deduced a certain projective \(G\)-resolution of \(k\), using a grading \(e:S\to\mathbb{N}\), an ordering of \(S\) such that \(e^{-1} (n)\) is well ordered for all \(n \in \mathbb{N}\), and the notion of an obstruction in the free monoid over \(S\). Here, the author proves the minimality of Anick's resolution under the assumption that \(S\) is a minimal set of generators contained in the augmentation ideal and that all obstructions are monomials of length 2.
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 55S10
zbMATH DE Number: 868028
zbMATH Keywords: augmented algebra
zbMATH Keywords: grading
zbMATH Keywords: projective resolution
MaRDI profile type: Publication
full work available at URL: jabr.1996.0044
OpenAlex ID: W2058892229
DOI: 10.1006/JABR.1996.0044
description: scientific article; zbMATH DE number 868028