一上同调与II_1因子群测度空间分解的唯一性
One-cohomology and the uniqueness of the group measure space decomposition of a II_1 factor
摘要：
我们提供了一个统一的和自包含的治疗最近的几个唯一性定理的群测度空间分解的II_1因子。我们提出了一类具有单上同调性质的群Γ，证明了对于Γ的每一个自由遍历概率测度保持作用，其对应的II_1因子具有唯一的群测度空间Cartan子代数，直到酉共轭.我们的方法密切遵循最近的一篇文章Chifan彼得森，但我们取代使用彼得森的无界导子托马斯辛克莱的膨胀成一个参数的自同构自同构群。
英文摘要：
We provide a unified and self-contained treatment of several of the recent uniqueness theorems for the group measure space decomposition of a II_1 factor. We single out a large class of groups Γ, characterized by a one-cohomology property, and prove that for every free ergodic probability measure preserving action of Γthe associated II_1 factor has a unique group measure space Cartan subalgebra up to unitary conjugacy. Our methods follow closely a recent article of Chifan-Peterson, but we replace the usage of Peterson's unbounded derivations by Thomas Sinclair's dilation into a one-parameter group of automorphisms.
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