| dc.contributor.advisor | Schick, Thomas Prof. Dr. | |
| dc.contributor.author | Brugger, Rahel | |
| dc.date.accessioned | 2018-05-02T09:08:53Z | |
| dc.date.available | 2018-05-02T09:08:53Z | |
| dc.date.issued | 2018-05-02 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E3D5-B | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-6832 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Characters on infinite groups and rigidity | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Schick, Thomas Prof. Dr. | |
| dc.date.examination | 2018-02-07 | |
| dc.description.abstracteng | We show that for a strong extension of discrete measured groupoids $1\to\mathcal{S}\to\mathcal{G}\to\mathcal{Q}\to 1$ with $L\mathcal{G}$ a finite factor, $\mathcal{Q}$ has poperty (T) if and only if the inclusion of $L\mathcal{S}$ into $L\mathcal{G}$ is corigid. In particular, this implies that $\mathcal{G}$ has property (T) if and only if $L^\infty(X)\subset L\mathcal{G}$ is corigid.
Furthermore, we give the definition of an invariant random positive definite function on a discrete group, generalizing both the notion of an Invariant Random Subgroup and a character. We use von Neumann algebras to show that all invariant random positive definite functions on groups with infinite conjugacy classes which integrate to the regular character are constant.
We also show a rigidity result for subfactors that are normalized by a representation of a lattice $\Gamma$ in a higher rank simple Lie group with trivial center into a finite factor. This implies that every subfactor of $L\Gamma$ which is normalized by the natural copy of $\Gamma$ is trivial or of finite index. | de |
| dc.contributor.coReferee | Meyer, Ralf Prof. Dr. | |
| dc.subject.eng | von Neumann algebras | de |
| dc.subject.eng | property (T) | de |
| dc.subject.eng | invariant random positive definite functions | de |
| dc.subject.eng | measured groupoids | de |
| dc.subject.eng | characters | de |
| dc.subject.eng | rigidity | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E3D5-B-0 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematik (PPN61756535X) | de |
| dc.identifier.ppn | 1022271962 | |