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Properly proximal groups and their von Neumann algebras

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBOUTONNET, Rémi
hal.structure.identifierMathematics Department; University of California San Diego
dc.contributor.authorIOANA, Adrian
hal.structure.identifierVanderbilt University [Nashville]
dc.contributor.authorPETERSON, Jesse
dc.date.accessioned2024-04-04T02:59:16Z
dc.date.available2024-04-04T02:59:16Z
dc.date.issued2021
dc.identifier.issn0012-9593
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192728
dc.description.abstractEnWe introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact groups, all non-elementary convergence groups, and all lattices in non-compact semi-simple Lie groups, but excludes all inner amenable groups. We show that crossed product II$_1$ factors arising from free ergodic probability measure preserving actions of groups in this class have at most one weakly compact Cartan subalgebra, up to unitary conjugacy. As an application, we obtain the first $W^*$-strong rigidity results for compact actions of $SL_d(\mathbb Z)$ for $d \geq 3$.
dc.language.isoen
dc.publisherSociété mathématique de France
dc.title.enProperly proximal groups and their von Neumann algebras
dc.typeArticle de revue
dc.identifier.doi10.24033/asens.2462
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halMathématiques [math]/Théorie des groupes [math.GR]
dc.subject.halMathématiques [math]/Algèbres d'opérateurs [math.OA]
dc.subject.halMathématiques [math]/Systèmes dynamiques [math.DS]
dc.identifier.arxiv1809.01881
bordeaux.journalAnnales Scientifiques de l'École Normale Supérieure
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02361525
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02361525v1
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