Extension of certain modules over the first Weyl algebra
type: Item
instance of: scholarly article
title: Extension of certain modules over the first Weyl algebra
zbMATH Open document ID: 0821.16033
author: Jie Xiao
author: Fred Van Oystaeyen
published in: Science in China. Series A
publication date: 1995-10-03T00:00:00Z
review text: The authors consider certain rather special finite length modules over the first Weyl algebra \(A_1 = k[x,d/dx]\), over a field of characteristic zero. They make use of an old result of McConnell and Robson computing \(\dim \text{Ext}(A_1/ (f + d/dx) A_1, A_1/ (g + d/dx) A_ 1) = 1\), for \(f, g \in k[x]\) with \(f - g\) of degree one. They use methods from the theory of finite dimensional algebras to investigate the category of finite length modules with composition factors isomorphic to \(A_1 / (f + d/dx) A_1\) or \(A_1/ (g + d/dx) A_1\). Specifically, they show that it corresponds to a tube of \(\mathbb{Z}/2 \mathbb{Z}\) type and that it is serial and standard.
reviewed by: Martin P. Holland
Mathematics Subject Classification ID: 16S32
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 640448
zbMATH Keywords: finite length modules
zbMATH Keywords: Weyl algebras
zbMATH Keywords: finite dimensional algebras
zbMATH Keywords: category of finite length modules
zbMATH Keywords: tubes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 640448