Free quasi-free states and factors of type III

Stefaan Vaes

Séminaire Bourbaki (2003-2004)

  • Volume: 46, page 329-350
  • ISSN: 0303-1179

Abstract

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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 1 in the classification of Connes.

How to cite

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Vaes, Stefaan. "États quasi-libres libres et facteurs de type III." Séminaire Bourbaki 46 (2003-2004): 329-350. <http://eudml.org/doc/252165>.

@article{Vaes2003-2004,
abstract = {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$_1$ dans la classification de Connes.},
author = {Vaes, Stefaan},
journal = {Séminaire Bourbaki},
keywords = {free probability theory; free Araki-Woods factors; classification of non-injective factors},
language = {fre},
pages = {329-350},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {États quasi-libres libres et facteurs de type III},
url = {http://eudml.org/doc/252165},
volume = {46},
year = {2003-2004},
}

TY - JOUR
AU - Vaes, Stefaan
TI - États quasi-libres libres et facteurs de type III
JO - Séminaire Bourbaki
PY - 2003-2004
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 46
SP - 329
EP - 350
AB - 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$_1$ dans la classification de Connes.
LA - fre
KW - free probability theory; free Araki-Woods factors; classification of non-injective factors
UR - http://eudml.org/doc/252165
ER -

References

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