Quasi-free states on the algebra of canonical anticommutation relations give rise to representations generating the injective Araki-Woods factors. In the framework of Voiculescu’s free probability theory, Shlyakhtenko has developed a free analogue of these Araki-Woods factors. Shlyakhtenko’s construction starts with a one-parameter group of orthogonal transformations of a real Hilbert space. The associated factors provide a rich class of new examples of non-injective factors of type III in the classification of Connes.
Les états quasi-libres sur l’algèbre des relations d’anticommutation canoniques donnent lieu à des représentations qui engendrent les facteurs moyennables d’Araki et Woods. Dans le cadre des probabilités libres de Voiculescu, Shlyakhtenko a trouvé un analogue libre de ces facteurs Araki-Woods. La construction de Shlyakhtenko part d’un groupe à un paramètre de transformations orthogonales d’un espace de Hilbert réel. Les facteurs associés fournissent une richesse de nouveaux exemples de facteurs de type III dans la classification de Connes.
Mot clés : probabilités libres, facteurs d'Araki-Woods libres, classification de facteurs non-injectifs
Keywords: free probability theory, free Araki-Woods factors, classification of non-injective factors
@incollection{SB_2003-2004__46__329_0, author = {Vaes, Stefaan}, title = {\'Etats quasi-libres libres et facteurs de type {III}}, booktitle = {S\'eminaire Bourbaki : volume 2003/2004, expos\'es 924-937}, series = {Ast\'erisque}, note = {talk:937}, pages = {329--350}, publisher = {Association des amis de Nicolas Bourbaki, Soci\'et\'e math\'ematique de France}, address = {Paris}, number = {299}, year = {2005}, mrnumber = {2167212}, zbl = {1091.46037}, language = {fr}, url = {http://archive.numdam.org/item/SB_2003-2004__46__329_0/} }
TY - CHAP AU - Vaes, Stefaan TI - États quasi-libres libres et facteurs de type III BT - Séminaire Bourbaki : volume 2003/2004, exposés 924-937 AU - Collectif T3 - Astérisque N1 - talk:937 PY - 2005 SP - 329 EP - 350 IS - 299 PB - Association des amis de Nicolas Bourbaki, Société mathématique de France PP - Paris UR - http://archive.numdam.org/item/SB_2003-2004__46__329_0/ LA - fr ID - SB_2003-2004__46__329_0 ER -
%0 Book Section %A Vaes, Stefaan %T États quasi-libres libres et facteurs de type III %B Séminaire Bourbaki : volume 2003/2004, exposés 924-937 %A Collectif %S Astérisque %Z talk:937 %D 2005 %P 329-350 %N 299 %I Association des amis de Nicolas Bourbaki, Société mathématique de France %C Paris %U http://archive.numdam.org/item/SB_2003-2004__46__329_0/ %G fr %F SB_2003-2004__46__329_0
Vaes, Stefaan. États quasi-libres libres et facteurs de type III, in Séminaire Bourbaki : volume 2003/2004, exposés 924-937, Astérisque, no. 299 (2005), Talk no. 937, pp. 329-350. http://archive.numdam.org/item/SB_2003-2004__46__329_0/
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