Rigid actions need not be strongly ergodic
Operator Algebras
2012-08-08 v3 Dynamical Systems
Group Theory
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.
Keywords
Cite
@article{arxiv.1006.4502,
title = {Rigid actions need not be strongly ergodic},
author = {Adrian Ioana and Stefaan Vaes},
journal= {arXiv preprint arXiv:1006.4502},
year = {2012}
}
Comments
v2: A comment has been added showing that rigid actions may admit non-rigid quotients v3: Minor changes; final version; to appear in Proc AMS