The source algebras of blocks with a Klein four defect group
type: Item
instance of: scholarly article
title: The source algebras of blocks with a Klein four defect group
zbMATH Open document ID: 0816.20013
author: Markus Linckelmann
published in: Journal of Algebra
publication date: 1994-10-12T00:00:00Z
review text: Let \(\mathcal O\) be a complete discrete valuation ring with algebraically closed residue field of characteristic 2, and let \(G\) be a finite group. The author shows that the source algebra of a 2-block of \(G\) with Klein four defect group \(P\) is isomorphic as an interior \(P\)-algebra to an iterated Heller translate of either \({\mathcal O}P\) or \({\mathcal O}A_ 4\) or to the principal block algebra of \({\mathcal O}A_ 5\) (where the Heller translate of an interior \(P\)-algebra is defined in terms of the \(\mathcal O\)- endomorphism ring of the Heller translate of the trivial module). This result extends the work of R. Brauer and K. Erdmann on such blocks.
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 638519
zbMATH Keywords: pointed groups
zbMATH Keywords: source algebras
zbMATH Keywords: 2-block
zbMATH Keywords: Klein four defect group
zbMATH Keywords: interior \(P\)-algebra
zbMATH Keywords: Heller translate
zbMATH Keywords: principal block algebra
MaRDI profile type: Publication
full work available at URL: jabr.1994.1214
OpenAlex ID: W1978719305
DOI: 10.1006/JABR.1994.1214
description: scientific article; zbMATH DE number 638519