Rigid actions need not be strongly ergodic

Details Rigid actions need not be strongly ergodic Rigid actions need not be strongly ergodic

2010-06-23

arxiv.org/abs/1006.4502v3

Mathematics

Operator Algebras

v2: A comment has been added showing that rigid actions may admit non-rigid quotients v3: Minor changes; final version; to app

Scientific paper

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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