A strong Connes spectrum for finite group actions of simple rings
type: Item
instance of: scholarly article
title: A strong Connes spectrum for finite group actions of simple rings
zbMATH Open document ID: 0736.16019
DOI: 10.1016/0021-8693(91)90317-2
author: James Osterburg
author: Costel Peligrad
published in: Journal of Algebra
publication date: 1992-06-26T00:00:00Z
review text: This is the second in a series of papers which develop algebraic analogs of the Connes spectrum. The first, by \textit{S. Montgomery} and the reviewer [J. Algebra 115, 92-124 (1988; Zbl 0639.16002)] studied the smash product \(A\#k[G]^*\) where \(k[G]^*\) is the dual of the group algebra \(k[G]\) of the finite group \(G\). This paper considers the skew group ring \(AG=A\#k[G]^*\) and obtains necessary and sufficient conditions for the ring to be simple in terms of the irreducible representations of \(G\). More recently, these results have been extended to the general Hopf algebra smash product situation in various papers by J. Osterburg, D. Quinn and the reviewer. In particular, there is now a general definition for the Connes spectrum of a finite dimensional Hopf algebra \(H\) acting on the \(H\)-module algebra \(A\) and there are necessary and sufficient conditions for the smash product \(A\# H\) to be prime or simple.
Mathematics Subject Classification ID: 16S35
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16S40
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 23608
zbMATH Keywords: Connes spectrum
zbMATH Keywords: smash product
zbMATH Keywords: skew group ring
zbMATH Keywords: irreducible representations
zbMATH Keywords: Hopf algebra smash product
zbMATH Keywords: finite dimensional Hopf algebra
reviewed by: D. S. Passman
MaRDI profile type: Publication
full work available at URL: 0021-8693(91)90317-2
OpenAlex ID: W1994319030
cites work: Modules with decompositions that complement direct summands
cites work: Algebras of spherical functions associated with covariant systems over a compact group.
cites work: Q3920162
cites work: Fixed rings of finite automorphism groups of associative rings
cites work: Algebraic analogs of the Connes spectrum
cites work: Locally compact group actions on \(C^ *\)-algebras and compact subgroups
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description: scientific article; zbMATH DE number 23608