Modules with simple multiplicity modules
type: Item
instance of: scholarly article
title: Modules with simple multiplicity modules
zbMATH Open document ID: 0832.20011
author: Laurence Barker
published in: Journal of Algebra
publication date: 1996-02-22T00:00:00Z
review text: Let \(G\) be a finite group, \(\mathcal O\) be a complete local commutative noetherian ring with an algebraically closed residue field \(k\) of nonzero characteristic \(p\). Let \(M\) be an indecomposable \({\mathcal O}G\)-module with vertex \(P\), \(\delta\) be a local point of \(P\) on \(\text{End}_{\mathcal O}(M)\) and \(V\) be the multiplicity \(k_*\widehat{\overline {N}}_G(P_\delta)\)-module of \(M\). In Section 1 the author gives some necessary and sufficient criteria for \(V\) to be simple. In Section 2 the author presents a reciprocity law which concerns direct summands of modules induced from, and modules restricted from, modules with simple multiplicity modules.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 763913
zbMATH Keywords: finite groups
zbMATH Keywords: simple modules
zbMATH Keywords: reciprocity law
zbMATH Keywords: direct summands
zbMATH Keywords: multiplicity modules
reviewed by: S. D. Kozlov
MaRDI profile type: Publication
full work available at URL: jabr.1995.1055
OpenAlex ID: W2027524549
DOI: 10.1006/JABR.1995.1055
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description: scientific article; zbMATH DE number 763913