论文标题
关于奇特$ W^*$ - 动力系统的紧凑型扩展
On compact extensions of tracial $W^*$-dynamical systems
论文作者
论文摘要
我们为奇特$ W^*$ - 动力学系统的紧凑型扩展以及相对独立的联接而建立了几个分类结果，以进行任意离散组的操作。我们使用这些结果来回答Austin，Eisner和Tao的问题，以及Duvenhage和King提出的一些问题。此外，将我们的结果与POPA的弱混合扩展分类相结合，我们可以在$ l^2 $ level上得出非交通性的Furstenberg-Zimmer型二分法。尽管总的来说，在冯·诺伊曼（Von Neumann）代数框架中，似乎不可能对中间紧凑型扩展的Furstenberg-Zimmer塔进行充分的概括，但我们表明，对于任何可计算值的亚伯里亚人组的任何可行的动作。
We establish several classification results for compact extensions of tracial $W^*$-dynamical systems and for relatively independent joinings thereof for actions of arbitrary discrete groups. We use these results to answer a question of Austin, Eisner, and Tao and some questions raised by Duvenhage and King. Moreover, combining our results with an earlier classification of weakly mixing extensions by Popa, we can derive non-commutative Furstenberg-Zimmer type dichotomies on the $L^2$-level. Although in general an adequate generalization of the Furstenberg-Zimmer tower of intermediate compact extensions doesn't seem possible in the von Neumann algebraic framework, we show that there always exists a non-commutative analogue of the finer Host-Kra-Ziegler tower for any ergodic action of a countable abelian group.
