Rigidity results for Bernoulli actions and their von Neumann algebras (after Sorin Popa)

Details Rigidity results for Bernoulli actions and their von Neumann algebras (after Sorin Popa) Rigidity results for Bernoulli actions and their von Neumann algebras (after Sorin Popa)

2006-03-17

arxiv.org/abs/math/0603434v2

Asterisque 311 (2007), 237-294

Mathematics

Operator Algebras

Minor corrections

Scientific paper

We survey Sorin Popa's recent work on Bernoulli actions. The paper was written on the occasion of the Bourbaki seminar. 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, yielding 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.

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