Strong Rigidity of II$_1$ Factors Arising from Malleable Actions of w-Rigid Groups, I
| dc.creator | Popa, Sorin | |
| dc.date | 2003-05-21 | |
| dc.date | 2005-06-02 | |
| dc.date.accessioned | 2026-07-07T04:58:11Z | |
| dc.date.available | 2026-07-07T04:58:11Z | |
| dc.description | We consider cross-product II$_1$ factors $M = N\rtimes_σ G$, with $G$ discrete ICC groups that contain infinite normal subgroups with the relative property (T) and $σ: G \to {\text{\rm Aut}}N$ trace preserving actions of $G$ on finite von Neumann algebras $N$ that are ``malleable'' and mixing. Examples are the weighted Bernoulli and Bogoliubov shifts. We prove a rigidity result for such factors, showing the uniqueness of the position of $L(G)$ inside $M$. We use this to calculate the fundamental group $\mycal F(M)$ in terms of the weights of the shift, for certain arithmetic groups $G$ such as $G=\Bbb Z^2 \rtimes SL(2, \Bbb Z)$. We deduce that for any countable group $S \subset \Bbb R_+^*$ there exist II$_1$ factors $M$ with $\mycal F(M)=S$, thus bringing new light to a longstanding problem of Murray and von Neumann. | |
| dc.description | revised version 40 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305306 | |
| dc.identifier | http://arxiv.org/abs/math/0305306 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67532 | |
| 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, I | |
| dc.type | text |