Actions of dense subgroups of compact groups and $\textrm{II}_1$-factors with the Haagerup property
| dc.creator | Jolissaint, Paul | |
| dc.date | 2005-10-14 | |
| dc.date.accessioned | 2026-07-07T06:47:29Z | |
| dc.date.available | 2026-07-07T06:47:29Z | |
| dc.description | Let $M$ be a finite von Neumann algebra with the Haagerup property, and let $G$ be a compact group that acts continuously on $M$ and that preserves some finite trace $τ$. We prove that if $Γ$ is a countable subgroup of $G$ which has the Haagerup property, then the crossed product algebra $M\rtimesΓ$ has also the Haagerup property. In particular, we study some ergodic, non-weakly mixing actions of groups with the Haagerup property on finite, injective von Neumann algebras, and we prove that the associated crossed products von Neumann algebras are $\textrm{II}_1$-factors with the Haagerup property. If moreover the actions have Property $(τ)$, then the latter factors are full. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510301 | |
| dc.identifier | http://arxiv.org/abs/math/0510301 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103669 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L10; 20H05;28D05 | |
| dc.title | Actions of dense subgroups of compact groups and $\textrm{II}_1$-factors with the Haagerup property | |
| dc.type | text |