Rigid actions need not be strongly ergodic (Q2845754)
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scientific article; zbMATH DE number 6203929
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rigid actions need not be strongly ergodic |
scientific article; zbMATH DE number 6203929 |
Statements
Rigid actions need not be strongly ergodic (English)
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3 September 2013
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ergodic action
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rigidity
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von Neumann algebra
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invariant measure
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This note contains a negative answer to the question posed by \textit{S. Popa} [Ann. Math. (2) 163, No. 3, 809--899 (2006; Zbl 1120.46045)] whether all rigid free ergodic probability measure preserving actions are strongly ergodic. The authors give examples of rigid free probability measures preserving actions that are ergodic but not strongly ergodic. The same examples show that rigid actions may admit non-rigid quotients.
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