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The Haagerup property for measure preserving standard equivalence relations
Date de parution
2005
In
Ergodic Theory and Dynamical Systems
No
25
De la page
161
A la page
174
Résumé
We define a notion of the Haagerup property for measure-preserving standard equivalence relations. Given such a relation R on X with finite invariant measure mu, we prove that R has the Haagerup property if and only if the associated finite von Neumann algebra L(R) (see J. Feldman and C. C. Moore. Ergodic equivalence relations, cohomology and von Neumann algebras II. Trans. Amer. Math. Soc. 234 (1977), 325-350) has relative property H in the sense of Popa with respect to its natural Cartan subalgebra L-infinity(X, mu). We also prove that if G is a countable group such that R = R-G has the Haagerup property and if R is ergodic, then G cannot have Kazhdan's property T.
Identifiants
Type de publication
journal article
