RIGIDITY FOR VON NEUMANN ALGEBRAS
RIGIDITY FOR VON NEUMANN ALGEBRAS
复制标题
冯·诺依曼代数的刚性
DOI：
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发表时间：
2017
期刊：
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通讯作者：
A. Ioana
中科院分区：
文献类型：
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作者：
A. Ioana
我们调查的一些进展，最近在分类的冯诺依曼代数所产生的可数群和他们的措施保持行动的概率空间。我们强调的结果，提供类（W$^*$-超刚性）的行动，可以完全恢复从他们的冯诺依曼代数和II$_1$因子，有一个独特的Cartan子代数。我们还提出了上圈超刚性定理和它们在轨道等价中的一些应用。最后，我们讨论了群上vonNeumann代数刚性的几个最新结果。
We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize results which provide classes of (W$^*$-superrigid) actions that can be completely recovered from their von Neumann algebras and II$_1$ factors that have a unique Cartan subalgebra. We also present cocycle superrigidity theorems and some of their applications to orbit equivalence. Finally, we discuss several recent rigidity results for von Neumann algebras associated to groups.