We study II factors and 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 --bimodule (in particular, every isomorphism between and ) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index --bimodules is identified with an extended Hecke fusion algebra, providing the first explicit computations of the fusion algebra of a II factor. We obtain in particular explicit examples of II factors with trivial fusion algebra, i.e. only having trivial finite index subfactors.
Nous étudions des facteurs et de type II associés à de bonnes actions Bernoulli généralisées de groupes et ayant un sous-groupe infini presque-distingué avec la propriété (T) relative. Nous démontrons le résultat de rigidité suivant : chaque --bimodule d’indice fini (en particulier, chaque isomorphisme entre et ) peut être décrit par une commensurabilité des groupes , et une commensurabilité de leurs actions. L’algèbre de fusion des --bimodules d’indice fini est identifiée avec une algèbre de Hecke étendue, ce qui fournit les premiers calculs explicites de l’algèbre de fusion d’un facteur de type II. Nous obtenons en particulier des exemples explicites de facteurs II dont l’algèbre de fusion est triviale, ce qui veut dire que tous leurs sous-facteurs d’indice fini sont triviaux.
@article{ASENS_2008_4_41_5_743_0, author = {Vaes, Stefaan}, title = {Explicit computations of all finite index bimodules for a family of {II}$_1$ factors}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {743--788}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 41}, number = {5}, year = {2008}, doi = {10.24033/asens.2081}, mrnumber = {2504433}, zbl = {1194.46086}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.2081/} }
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 SP - 743 EP - 788 VL - 41 IS - 5 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/asens.2081/ DO - 10.24033/asens.2081 LA - en ID - ASENS_2008_4_41_5_743_0 ER -
%0 Journal Article %A Vaes, Stefaan %T Explicit computations of all finite index bimodules for a family of II$_1$ factors %J Annales scientifiques de l'École Normale Supérieure %D 2008 %P 743-788 %V 41 %N 5 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/asens.2081/ %R 10.24033/asens.2081 %G en %F ASENS_2008_4_41_5_743_0
Vaes, Stefaan. Explicit computations of all finite index bimodules for a family of II$_1$ factors. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 5, pp. 743-788. doi : 10.24033/asens.2081. http://archive.numdam.org/articles/10.24033/asens.2081/
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