On Thévenaz' parametrization of interior \(G\)-algebras
type: Item
instance of: scholarly article
title: On Thévenaz' parametrization of interior \(G\)-algebras
zbMATH Open document ID: 0798.20006
DOI: 10.1007/BF02571717
author: Lluis Puig
published in: Mathematische Zeitschrift
publication date: 1994-11-09T00:00:00Z
full work available at URL: https://eudml.org/doc/174615
review text: We give a complete proof of the parametrization of primitive interior \(G\)-algebras by the \(G\)-conjugacy classes of triples \((P,B,V)\) formed by a defect group \(P\), a \(P\)-source algebra \(B\) and a \((P,B)\)-multiplicity module \(V\), more or less suggested in Lemma 9.9 and Remarks 9.10 and 9.11 in an earlier paper [J. Algebra 116, No. 1, 7-129 (1988; Zbl 0658.20004)]. Moreover, for any primitive interior \(G\)-algebra being associated with a block of \(G\), we show how to replace the multiplicity module \(V\) -- which involves \(C_ G(P)\) and, consequently, is not an invariant of the block -- by suitable block invariants.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 567405
zbMATH Keywords: multiplicity module
zbMATH Keywords: source algebra
zbMATH Keywords: primitive interior \(G\)-algebras
zbMATH Keywords: defect group
zbMATH Keywords: block invariants
MaRDI profile type: Publication
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Wikidata QID: Q126270953
description: scientific article; zbMATH DE number 567405