Source algebras of \(p\)-central group extensions
type: Item
instance of: scholarly article
title: Source algebras of \(p\)-central group extensions
zbMATH Open document ID: 0974.20003
author: Lluis Puig
published in: Journal of Algebra
publication date: 2001-09-03T00:00:00Z
review text: Let \(p\) be a prime, \(k\) an algebraically closed of characteristic \(p\), and \(\mathcal O\) a complete discrete valuation ring with residue field \(k\). Previously, the author [Invent. Math. 93, No. 1, 77-116 (1988; Zbl 0646.20010)] showed the rigidity of the source algebra of a block \(b\) of a finite group \(G\) in the class of \({\mathcal O}P\)-interior algebras having a \(P\times P\) stable \(\mathcal O\)-basis, where \(P\) is a defect group for \(b\). In the present paper, a stronger uniqueness is demonstrated, in essence, even its reduction via a central \(p\)-subgroup determines the source algebra of a block. The proof uses the theory of semicovering homomorphisms, and is motivated by the author's notion of \({\mathcal O}^*\)-groups. This is a long paper in which experts in the area will find much of interest.
Mathematics Subject Classification ID: 20C11
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 1563185
zbMATH Keywords: source algebras
zbMATH Keywords: blocks
zbMATH Keywords: defect groups
zbMATH Keywords: Brauer categories
zbMATH Keywords: semicovering homomorphisms
zbMATH Keywords: Frobenius categories
zbMATH Keywords: pointed groups
zbMATH Keywords: \({\mathcal O}^*\)-groups
zbMATH Keywords: interior algebras
reviewed by: William H. Gustafson
MaRDI profile type: Publication
full work available at URL: jabr.2000.8474
OpenAlex ID: W1988856049
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DOI: 10.1006/JABR.2000.8474
description: scientific article; zbMATH DE number 1563185