Blocks and indecomposable modules over twisted group algebras
type: Item
instance of: scholarly article
title: Blocks and indecomposable modules over twisted group algebras
zbMATH Open document ID: 0563.20012
DOI: 10.1007/BF01195368
author: J. Blot
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: Let G be a finite group, let F be an arbitrary field of characteristic \(p>0\), and let \(\alpha \in Z^ 2(G,F^*)\). Denote by \(F^{\alpha}G\) the corresponding twisted group algebra. The aim of this paper is to establish the following generalization of a theorem of \textit{J. A. Green} [Math. Z. 79, 100-115 (1962; Zbl 0233.20006)]. Theorem. Let B be a block of \(F^{\alpha}G\) with defect group D and let \(\Delta\) : \(g\to (g,g)\) be the diagonal map of G into \(G\times G\). Define \(\alpha^{-1}\times \alpha: (G\times G)\times (G\times G)\to F^*\) by \((\alpha^{-1}\times \alpha)((g_ 1,g_ 2),(g'\!_ 1,g'\!_ 2))=\alpha^{-1}(g_ 1,g'\!_ 1)\alpha (g_ 2,g'\!_ 2).\) Then the indecomposable \(F^{\alpha^{-1}\times \alpha}(G\times G)\)-module B has vertex \(\Delta\) (D). Furthermore, D is an intersection of two Sylow p-subgroups of G.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C25
zbMATH DE Number: 3897195
zbMATH Keywords: finite group
zbMATH Keywords: twisted group algebra
zbMATH Keywords: block
zbMATH Keywords: defect group
zbMATH Keywords: vertex
zbMATH Keywords: Sylow p-subgroups
MaRDI profile type: Publication
cites work: Twisted group algebras and their representations
cites work: Blocks of modular representations
cites work: Q3934684
cites work: Q3684285
cites work: Blocks and centres of group algebras
full work available at URL: https://doi.org/10.1007/bf01195368
OpenAlex ID: W2008324370
description: scientific article; zbMATH DE number 3897195