Strong rigidity of II$_1$ factors arising from malleable actions of w-rigid groups, II
| dc.creator | Popa, Sorin | |
| dc.date | 2004-07-07 | |
| dc.date | 2005-05-31 | |
| dc.date.accessioned | 2026-07-07T05:10:01Z | |
| dc.date.available | 2026-07-07T05:10:01Z | |
| dc.description | We prove that any isomorphism $θ:M_0\simeq M$ of group measure space II$_1$ factors, $M_0=L^\infty(X_0, μ_0) \rtimes_{σ_0} G_0$, $M=L^\infty(X, μ) \rtimes_σ G$, with $G_0$ containing infinite normal subgroups with the relative property (T) of Kazhdan-Margulis (i.e. $G_0$ {\it w-rigid}) and $G$ an ICC group acting by Bernoulli shifts $σ$, essentially comes from an isomorphism of probability spaces which conjugates the actions. Moreover, any isomorphism $θ$ of $M_0$ onto a ``corner'' $pMp$ of $M$, for $p\in M$ an idempotent, forces $p=1$. In particular, all group measure space factors associated with Bernoulli shift actions of w-rigid ICC groups have trivial fundamental group and all isomorphisms between such factors come from isomorphisms of the corresponding groups. This settles a ``group measure space version'' of Connes rigidity conjecture, shown in fact to hold true in a greater generality than just for ICC property (T) groups. We apply these results to ergodic theory, establishing new strong rigidity and superrigidity results for orbit equivalence relations. | |
| dc.description | Sequel Part II of the paper with the same title math.OA/0305306. 45 pages | |
| dc.identifier | https://arxiv.org/abs/math/0407103 | |
| dc.identifier | http://arxiv.org/abs/math/0407103 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71801 | |
| dc.subject | Operator Algebras | |
| dc.subject | Group Theory | |
| dc.subject | 46L55, 46L10, 46L40, 22D25, 22D40, 28D15 | |
| dc.title | Strong rigidity of II$_1$ factors arising from malleable actions of w-rigid groups, II | |
| dc.type | text |