The isomorphism problem for cyclic blocks and their source algebras
type: Item
instance of: scholarly article
title: The isomorphism problem for cyclic blocks and their source algebras
zbMATH Open document ID: 0865.20009
author: Markus Linckelmann
published in: Inventiones Mathematicae
publication date: 1997-07-15T00:00:00Z
review text: The structure of blocks with cyclic defect groups is determined in terms of their source algebras, thus confirming a conjecture of the author that the source algebras of such a block are essentially determined by an endo-permutation module of the defect group and the Brauer tree of the block. In fact, it is shown that blocks satisfy an analog of the isomorphism problem for group algebras. Thus, normalizing suitably, the group of units of the block algebra has a unique conjugacy class of subgroups isomorphic to the defect group.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16U60
zbMATH DE Number: 922466
zbMATH Keywords: cyclic defect groups
zbMATH Keywords: source algebras
zbMATH Keywords: endo-permutation modules
zbMATH Keywords: Brauer trees
zbMATH Keywords: isomorphism problem for group algebras
zbMATH Keywords: groups of units
reviewed by: William H. Gustafson
MaRDI profile type: Publication
full work available at URL: s002220050075
OpenAlex ID: W2042428977
DOI: 10.1007/S002220050075
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description: scientific article; zbMATH DE number 922466