L^2-rigidity in von Neumann algebras
| dc.creator | Peterson, Jesse | |
| dc.date | 2006-05-01 | |
| dc.date.accessioned | 2026-07-07T07:13:48Z | |
| dc.date.available | 2026-07-07T07:13:48Z | |
| dc.description | We introduce the notion of L^2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L^2-rigidity passes to normalizers and is satisfied by nonamenable II_1 factors which are non-prime, have property $Γ$, or are weakly rigid. As a consequence we obtain that if $M$ is a free product of diffuse von Neumann algebras, or if $M = LΓ$ where $Γ$ is a finitely generated group with $b_1^{(2)}(Γ) > 0$, then any nonamenable regular subfactor of $M$ is prime and does not have properties $Γ$ or (T). In particular this gives a new approach for showing primeness of all nonamenable subfactors of a free group factor thus recovering a well known recent result of N. Ozawa. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0605033 | |
| dc.identifier | http://arxiv.org/abs/math/0605033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112613 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L10 (Primary) 46L57, 46L54 (Secondary) | |
| dc.title | L^2-rigidity in von Neumann algebras | |
| dc.type | text |