Stability for integer actions on UHF \(C^*\)-algebras (Q1066429)
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scientific article; zbMATH DE number 3925596
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability for integer actions on UHF \(C^*\)-algebras |
scientific article; zbMATH DE number 3925596 |
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Stability for integer actions on UHF \(C^*\)-algebras (English)
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1984
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\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.
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1-cohomology
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cyclic product actions on any UHF \(C^*\)-algebra
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complete set of invariants for conjugacy and outer conjugacy
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Glimm-type invariant
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