Cohomology operators defined by a deformation
type: Item
instance of: scholarly article
title: Cohomology operators defined by a deformation
zbMATH Open document ID: 0915.13009
author: Luchezar L. Avramov
author: Li-Chuan Sun
published in: Journal of Algebra
publication date: 1999-07-07T00:00:00Z
review text: By viewing \(R\)-modules as differential graded modules over the Koszul complex resolving \(R\) over \(\mathbb{Q}\), the authors construct cohomology operators \(\chi_j:\text{Ext}^i_R(M,N)\to\text{Ext}^{i+1}_R(M,N)\) and \(\text{Tor}_i^K(L,M)\to\text{Tor}^K_{i-2}(L,M)\) and establish their main properties directly for complexes of \(R\)-modules. They give two different approaches, first à la Gulliksen, as connecting homomorphisms, second from chain-level maps, as did Eisenbud. The authors give direct proofs of their formal properties and in particular of their centrality. They compare the operators \(\chi_j\) to the cohomology operators previously constructed by Gulliksen, Eisenbud, Mehta and Avramov.
Mathematics Subject Classification ID: 13D10
Mathematics Subject Classification ID: 13D25
Mathematics Subject Classification ID: 13D03
zbMATH DE Number: 1218680
zbMATH Keywords: differential graded modules
zbMATH Keywords: complexes of modules
zbMATH Keywords: cohomology operators
reviewed by: Yves Félix
MaRDI profile type: Publication
OpenAlex ID: W1991132465
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DOI: 10.1006/JABR.1997.7317
description: scientific article; zbMATH DE number 1218680