On stable equivalences and blocks with one simple module.
type: Item
instance of: scholarly article
title: On stable equivalences and blocks with one simple module.
zbMATH Open document ID: 1196.20013
author: Radha Kessar
author: Markus Linckelmann
published in: Journal of Algebra
publication date: 2010-03-29T00:00:00Z
full work available at URL: onesimple.pdf
review text: Let \(p\) be a prime, and let \(B\) be a \(p\)-block of a finite group \(G\) with a defect group \(D\) of order \(|D|\leq p^2\). Suppose that the Brauer correspondent \(C\) of \(B\) has precisely one irreducible Brauer character. The authors show that there is a \(p\)-permutation equivalence between \(B\) and \(C\) inducing an isotypy. In particular, \(B\) has also precisely one irreducible Brauer character, and the decomposition numbers of \(B\) and \(C\) coincide. -- One of the main tools in their proof is a stable equivalence constructed by Rouquier.
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 5687627
zbMATH Keywords: blocks
zbMATH Keywords: defect groups
zbMATH Keywords: perfect isometries
zbMATH Keywords: decomposition numbers
zbMATH Keywords: Alperin weight conjecture
zbMATH Keywords: irreducible Brauer characters
MaRDI profile type: Publication
OpenAlex ID: W1995011984
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DOI: 10.1016/J.JALGEBRA.2010.01.006
description: scientific article; zbMATH DE number 5687627