Quasi-product actions of a compact group on a \(C^*\)-algebra
type: Item
instance of: scholarly article
title: Quasi-product actions of a compact group on a \(C^*\)-algebra
zbMATH Open document ID: 0813.46058
author: Ola Bratteli
author: Akitaka Kishimoto
author: George A. Elliott
published in: Journal of Functional Analysis
publication date: 1995-05-28T00:00:00Z
review text: Let \(\alpha\) be an action of a compact group on a separable prime \(C^*\)-algebra \(A\). The authors prove several conditions on \(\alpha\) to be equivalent, among which are the following two: there exists a faithful irreducible representation of \(A\) which is also irreducible on \(A^ \alpha\); there exists an \(\alpha\)-invariant pure state \(\omega\) of \(A\) such that \(\pi_{\omega\mid A^ \alpha}\) is faithful (it follows also that \(\pi_ \omega\) is faithful). These two conditions mean, roughly speaking, that there exists, respectively, free orbits and fixed points in the space of equivalence classes of irreducible representations of \(A\), acted upon by \(G\).
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 22D25
zbMATH DE Number: 515232
zbMATH Keywords: invariant pure state
zbMATH Keywords: action of a compact group on a separable prime \(C^*\)-algebra
zbMATH Keywords: faithful irreducible representation
zbMATH Keywords: free orbits
zbMATH Keywords: fixed points
zbMATH Keywords: space of equivalence classes of irreducible representations
MaRDI profile type: Publication
full work available at URL: jfan.1993.1093
OpenAlex ID: W2092090143
DOI: 10.1006/JFAN.1993.1093
description: scientific article; zbMATH DE number 515232