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arXiv math/06034342006-03math.OAmath.GR

Bernoulli作用及其von Neumann algebras的刚性结果（根据Sorin Popa）

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

Stefaan Vaes

备注：: Minor corrections
发表信息：: Asterisque 311 (2007), 237-294

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摘要：

我们调查索林波帕最近的工作伯努利行动。这篇论文是在布尔巴基研讨会上写的。使用非常原始的方法从算子代数，索林波帕已表明，轨道结构的伯努利行动的性质（T）组，完全记得集团和行动。这些信息甚至基本上包含在交叉积冯诺依曼代数中，产生了文献中的第一个冯诺依曼强刚性定理。同样的方法允许Popa获得II_1因子与规定的可数基本群。

英文摘要：

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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