Stability for integer actions on UHF \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Stability for integer actions on UHF \(C^*\)-algebras
zbMATH Open document ID: 0578.46058
DOI: 10.1016/0022-1236(84)90056-9
author: Richard H. Herman
author: Adrian Ocneanu
published in: Journal of Functional Analysis
publication date: 1984-01-01T00:00:00Z
review text: \textit{A. Connes} has given in Acta Sci. Math. 39, 39-66 (1977; Zbl 0382.46027)] a classification of \(Z_ n\) actions on the hyperfinite \(II_ 1\) factor. The authors obtain a norm-continuous version of Connes' solution to 1-cohomology which is adaptable to the \(C^*\)-algebra situation. They also exhibit various model actions which are stable. For the cyclic product actions on any UHF \(C^*\)-algebra they give a complete set of invariants for conjugacy and outer conjugacy. A Glimm- type invariant enters for conjugacy.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 3925596
zbMATH Keywords: 1-cohomology
zbMATH Keywords: cyclic product actions on any UHF \(C^*\)-algebra
zbMATH Keywords: complete set of invariants for conjugacy and outer conjugacy
zbMATH Keywords: Glimm-type invariant
MaRDI profile type: Publication
full work available at URL: 0022-1236(84)90056-9
OpenAlex ID: W1966125375
cites work: Q4161729
cites work: Outer conjugacy classes of automorphisms of factors
cites work: On some \(C^ *\)-algebras considered by Glimm
cites work: On a Certain Class of Operator Algebras
cites work: Period two automorphisms of UHF C*-algebras
cites work: Models of finite group actions.
cites work: Action of discrete amenable groups on von Neumann algebras
cites work: Theory of operator algebras I.
description: scientific article; zbMATH DE number 3925596