# Explicit computations of all finite index bimodules for a family of II${}_{1}$ factors

Annales scientifiques de l'École Normale Supérieure (2008)

- Volume: 41, Issue: 5, page 743-788
- ISSN: 0012-9593

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topVaes, Stefaan. "Explicit computations of all finite index bimodules for a family of II$_1$ factors." Annales scientifiques de l'École Normale Supérieure 41.5 (2008): 743-788. <http://eudml.org/doc/272130>.

@article{Vaes2008,

abstract = {We study II$_1$ factors $M$ and $N$ associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index $M$-$N$-bimodule (in particular, every isomorphism between $M$ and $N$) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index $M$-$M$-bimodules is identified with an extended Hecke fusion algebra, providing the first explicit computations of the fusion algebra of a II$_1$ factor. We obtain in particular explicit examples of II$_1$ factors with trivial fusion algebra, i.e. only having trivial finite index subfactors.},

author = {Vaes, Stefaan},

journal = {Annales scientifiques de l'École Normale Supérieure},

keywords = {generalized Bernoulli actions; good actions of good groups; II factors; fusion algebra; outer automorphism group; minimal condition on stabilizers},

language = {eng},

number = {5},

pages = {743-788},

publisher = {Société mathématique de France},

title = {Explicit computations of all finite index bimodules for a family of II$_1$ factors},

url = {http://eudml.org/doc/272130},

volume = {41},

year = {2008},

}

TY - JOUR

AU - Vaes, Stefaan

TI - Explicit computations of all finite index bimodules for a family of II$_1$ factors

JO - Annales scientifiques de l'École Normale Supérieure

PY - 2008

PB - Société mathématique de France

VL - 41

IS - 5

SP - 743

EP - 788

AB - We study II$_1$ factors $M$ and $N$ associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index $M$-$N$-bimodule (in particular, every isomorphism between $M$ and $N$) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index $M$-$M$-bimodules is identified with an extended Hecke fusion algebra, providing the first explicit computations of the fusion algebra of a II$_1$ factor. We obtain in particular explicit examples of II$_1$ factors with trivial fusion algebra, i.e. only having trivial finite index subfactors.

LA - eng

KW - generalized Bernoulli actions; good actions of good groups; II factors; fusion algebra; outer automorphism group; minimal condition on stabilizers

UR - http://eudml.org/doc/272130

ER -

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