Rigidity results for Bernoulli actions and their von Neumann algebras

Stefaan Vaes

Séminaire Bourbaki (2005-2006)

  • Volume: 48, page 237-294
  • ISSN: 0303-1179

Abstract

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Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II 1 factors with prescribed countable fundamental group.

How to cite

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Vaes, Stefaan. "Rigidity results for Bernoulli actions and their von Neumann algebras." Séminaire Bourbaki 48 (2005-2006): 237-294. <http://eudml.org/doc/252180>.

@article{Vaes2005-2006,
abstract = {Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II$_1$ factors with prescribed countable fundamental group.},
author = {Vaes, Stefaan},
journal = {Séminaire Bourbaki},
keywords = {superrigidity; Bernoulli action; property (T); classification of von Neumann algebras; II$_1$ factor; fundamental group},
language = {eng},
pages = {237-294},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Rigidity results for Bernoulli actions and their von Neumann algebras},
url = {http://eudml.org/doc/252180},
volume = {48},
year = {2005-2006},
}

TY - JOUR
AU - Vaes, Stefaan
TI - Rigidity results for Bernoulli actions and their von Neumann algebras
JO - Séminaire Bourbaki
PY - 2005-2006
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 48
SP - 237
EP - 294
AB - Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II$_1$ factors with prescribed countable fundamental group.
LA - eng
KW - superrigidity; Bernoulli action; property (T); classification of von Neumann algebras; II$_1$ factor; fundamental group
UR - http://eudml.org/doc/252180
ER -

References

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