Modules of codimension one over Weyl algebras
type: Item
instance of: scholarly article
title: Modules of codimension one over Weyl algebras
zbMATH Open document ID: 0863.16017
author: S. C. Coutinho
published in: Journal of Algebra
publication date: 1997-04-23T00:00:00Z
review text: This paper studies the structure of the category of all modules over a Weyl algebra with a characteristic variety which is a generic hypersurface, and therefore all its objects have Gelfand-Kirillov codimension one. An introduction and some basic results are proved in the first two sections. In section 3 it is proven that this category has infinitely many non-isomorphic irreducible modules of every possible multiplicity. In section 4 the first extension groups for some irreducible modules are calculated, and the author shows that \(\text{Ext}^1(M,N)\) may be infinite dimensional in contrast with the holonomic case. In the least section, the previous results are used to construct families of non-cyclic projective ideals for the Weyl algebra.
Mathematics Subject Classification ID: 16S32
Mathematics Subject Classification ID: 16P90
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 13N10
zbMATH DE Number: 848963
zbMATH Keywords: categories of modules
zbMATH Keywords: Weyl algebras
zbMATH Keywords: characteristic varieties
zbMATH Keywords: generic hypersurfaces
zbMATH Keywords: Gelfand-Kirillov codimension
zbMATH Keywords: irreducible modules
zbMATH Keywords: projective ideals
reviewed by: João B. Prolla
MaRDI profile type: Publication
full work available at URL: jabr.1995.1287
OpenAlex ID: W2047103350
DOI: 10.1006/JABR.1995.1287
description: scientific article; zbMATH DE number 848963