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H 2 Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions

Auteurs : Vaes, Stefaan (Auteur de la Conférence)
CIRM (Editeur )

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subfactors crosssed products symmetric enveloping algebra quasi-regular inclusions bar resolution $L^2$-cohomology tube algebra EXT and TOR amenable inclusions free products and tensor products TLJ subfactors representation theory Haagerup property and property (T) question of the audience

Résumé : I present a joint work with S. Popa and D. Shlyakhtenko introducing a cohomology theory for quasi-regular inclusions of von Neumann algebras. In particular, we define $L^2$-cohomology and $L^2$-Betti numbers for such inclusions. Applying this to the symmetric enveloping inclusion of a finite index subfactor, we get a cohomology theory and a definition of $L^2$-Betti numbers for finite index subfactors, as well as for arbitrary rigid $C^*$-tensor categories. For the inclusion of a Cartan subalgebra in a $II_1$ factor, we recover Gaboriau’s $L^2$-Betti numbers for equivalence relations.

Codes MSC :
46L10 - General theory of von Neumann algebras
46L37 - Subfactors and their classification

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 02/12/15
    Date de captation : 03/11/15
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:50:15
    Domaine : Analyse & Applications
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2015-11-03_Vaes.mp4

Informations sur la rencontre

Nom du congrès : Conference on noncommutative geometry / Conférence de géométrie non commutative
Organisteurs Congrès : Debord, Claire ; Le Gall, Pierre-Yves ; Tu, Jean-Louis ; Vaes, Stefaan ; Vassout, Stéphane ; Vergnioux, Roland
Dates : 02/11/15 - 06/11/15
Année de la rencontre : 2015
URL Congrès : http://conferences.cirm-math.fr/1206.html

Citation Data

DOI : 10.24350/CIRM.V.18879303
Cite this video as: Vaes, Stefaan (2015). Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18879303
URI : http://dx.doi.org/10.24350/CIRM.V.18879303


  1. Popa, S., Shlyakhtenko, D., Vaes, S. (2015). Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions. - http://arxiv.org/abs/1511.07329