Regularizations of twisted covariant systems and crossed products with continuous trace
type: Item
instance of: scholarly article
title: Regularizations of twisted covariant systems and crossed products with continuous trace
zbMATH Open document ID: 0801.46076
author: Siegfried Echterhoff
published in: Journal of Functional Analysis
publication date: 1994-11-24T00:00:00Z
review text: Given a twisted covariant system \((G, A, \tau)\), it is not easy to determine the topology of the primitive ideal space. In order to improve this situation, the author defines a regularization of \((G, A, \tau)\) as a pair \((\Omega, R)\) of a locally compact space \(\Omega\) and a continuous \(G\)-equivariant map \(R\) from Prim \((A)\) into \(\Omega\). He shows that regularization can be a useful tool for determining the structure of twisted crossed products. This is particularly the case when \(\Omega\) is a locally \(\sigma\)-trivial \(G\)-space: then each element in \(C^*(G, A, \tau)^ \wedge\) has a neighbourhood which can be described in terms of an appropriate subgroup algebra. In particular induced systems are exactly those which have \(\sigma\)-trivial regularizations where \(R\) is open and surjective. On the other hand, regularization allows to investigate whether certain crossed products have continuous trace.
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 515259
zbMATH Keywords: \(\sigma\)-trivial regularizations
zbMATH Keywords: twisted covariant system
zbMATH Keywords: topology of the primitive ideal space
zbMATH Keywords: induced systems
reviewed by: G. Loupias
MaRDI profile type: Publication
full work available at URL: jfan.1993.1114
OpenAlex ID: W1999728949
DOI: 10.1006/JFAN.1993.1114
description: scientific article; zbMATH DE number 515259