Noncommutative deformations of modules
type: Item
instance of: scholarly article
title: Noncommutative deformations of modules
zbMATH Open document ID: 1013.16018
published in: Homology, Homotopy and Applications
publication date: 2002-08-01T00:00:00Z
full work available at URL: https://eudml.org/doc/50047
full work available at URL: volume4-2-2.htm
review text: A non commutative deformation theory for modules on \(k\)-algebras is proposed and studied. First, the author introduces a deformation functor on the category of Artinian \(r\)-pointed not necessarily commutative \(k\)-algebras, generalizing the ordinary deformation functor as defined for instance by \textit{M. Schlessinger} [in Trans. Am. Math. Soc. 130, 208-222 (1968; Zbl 0167.49503)]. It is then proved that the generalized functor has a prorepresenting hull, which can be computed in terms of Ext-groups and their matric Massey products. A generalized Burnside theorem is then given. Finally, the general problem of classification of iterated extensions of a family of modules is studied and projects for forthcoming papers are described.
Mathematics Subject Classification ID: 16S80
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16G70
zbMATH DE Number: 1770081
zbMATH Keywords: deformations of modules
zbMATH Keywords: Hochschild cohomology
zbMATH Keywords: deformation functors
zbMATH Keywords: Artin algebras
zbMATH Keywords: Massey products
zbMATH Keywords: iterated extensions
author: Olav Arnfinn Laudal
reviewed by: Angela Gammella-Mathieu
MaRDI profile type: Publication
OpenAlex ID: W2119936144
DOI: 10.4310/HHA.2002.V4.N2.A17
description: scientific article; zbMATH DE number 1770081