On stable orthogonal decompositions of idempotents
type: Item
instance of: scholarly article
title: On stable orthogonal decompositions of idempotents
zbMATH Open document ID: 0976.20007
author: Yun Fan
author: Burkhard Külshammer
published in: Journal of Algebra
publication date: 2001-09-18T00:00:00Z
review text: The paper is concerned with Green's indecomposability theorem which asserts that the induced module of an absolutely indecomposable module from a subnormal subgroup of \(p\)-primary index is absolutely indecomposable. The authors are using here \textit{L. Puig}'s approach [Math. Z. 166, 117-129 (1979; Zbl 0395.16006)] to prove a generalization of Green's theorem to the case of an arbitrary complete discrete valuation ring \(\mathcal O\) with residue field \(k\) of characteristic \(p\). They prove general results characterizing the freeness relative to a subnormal subgroup of a relative projective pointed group on a \(G\)-algebra. If the subnormal subgroup has \(p\)-primary index, then the condition is satisfied if \(p\) does not divide the degree of a certain separable extension of \(k\).
reviewed by: Andrei Marcus
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 19A22
Mathematics Subject Classification ID: 20C25
zbMATH DE Number: 1340569
zbMATH Keywords: \(G\)-algebras
zbMATH Keywords: pointed groups
zbMATH Keywords: twisted group algebras
zbMATH Keywords: indecomposable modules
zbMATH Keywords: Green's indecomposability theorem
zbMATH Keywords: subnormal subgroups
MaRDI profile type: Publication
full work available at URL: jabr.1998.7820
OpenAlex ID: W1970494654
cites work: Q3722697
cites work: Induction, restriction and G-algebras
cites work: \(G\)-algebras, Clifford theory, and the Green correspondence
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cites work: Sur l'induction des modules indécomposables et la projectivité rélative
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cites work: Sur un théorème de Green
cites work: Pointed groups and construction of characters
cites work: Lifting idempotents and Clifford theory
cites work: Q4846455
DOI: 10.1006/JABR.1998.7820
description: scientific article; zbMATH DE number 1340569