Abstract
A probability measure preserving action of Γon (X,μ) is called rigid if the inclusion of L^\infty(X) into the crossed product L^\infty(X) \rtimes Γhas the relative property (T) in the sense of Popa. We give examples of rigid, free, probability measure 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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