Rigid actions need not be strongly ergodic

Adrian Ioana; Stefaan Vaes

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arXiv · 1006.4502

Rigid actions need not be strongly ergodic

Adrian Ioana·Stefaan Vaes

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Abstract

A probability measure preserving action of \Gamma on (X,\mu) is called rigid if the inclusion of L^\infty(X) into the crossed product L^\infty(X) \rtimes \Gamma has 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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Adrian Ioana, Stefaan Vaes. 2010-06-23. Rigid actions need not be strongly ergodic. https://arxiv.org/abs/1006.4502

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