Wild categories of periodic modules
type: Item
instance of: scholarly article
title: Wild categories of periodic modules
zbMATH Open document ID: 0664.20005
author: Alfredo Jones
author: Jon F. Carlson
published in: Illinois Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let K be a field of characteristic \(p>0\) and let G be an elementary abelian group of order \(p^ 2\). If \(p>2\), the result of \textit{A. Heller} and \textit{I. Reiner} [Ill. J. Math. 5, 314-323 (1961; Zbl 0111.031)] asserts that the category of left KG-modules is wild. Basically this means that there is no possibility of classifying the indecomposable objects in the category. Now assume that \(p>7\) and that \(\zeta\) is the Bockstein of a nonzero element of \(H^ 1(G,F_ p)\). If \(C_{\zeta}\) is the full subcategory of KG-modules M with \(\zeta \cdot Ext^*_{KG}(M,M)=0\), then it is shown here that \(C_{\zeta}\) is also wild.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16B50
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 4085883
zbMATH Keywords: elementary abelian group
zbMATH Keywords: category of left KG-modules
zbMATH Keywords: indecomposable objects
zbMATH Keywords: Bockstein
reviewed by: D. S. Passman
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4085883