von Neumann algebras上的Haagerup性质和作用
The Haagerup property and actions on von Neumann algebras
摘要：
在第2章的“团体与Haagerup财产”，Jolissaint一方面给了一个表征的Haagerup财产方面的强烈混合行动的标准概率空间;另一方面，他给了一个非交换模拟这一结果方面的行动的因素。在最近的文章“A new characterization of the Haagerup property by actions on infinite measure spaces“中，作者给出了Haagerup property的一个刻画，但这次是处理无限测度空间上的$C_0$ -作用.根据这一节的精神，我们给出了von Neumann代数上的$C_0$ -作用的一个非交换类似。接下来我们讨论围绕$C_0$ -动力系统的一些自然问题。特别是，我们给出的例子$C_0$ -动力系统的群体适当的树木。最后，我们对非周期群系统的遍历性问题给出了肯定的回答。
英文摘要：
In Chapter 2 of "Groups with the Haagerup Property", Jolissaint gives on the one hand a characterization of the Haagerup property in terms of strongly mixing actions on standard probability spaces; on the other hand he gives a noncommutative analogue of this result in terms of actions on factors. In the recent paper "A new characterization of the Haagerup property by actions on infinite measure spaces", the authors give a characterization of the Haagerup property but this time dealing with $C_0$-actions on infinite measure spaces. Following the spirit of this section, we give a noncommutative analogue in terms of $C_0$-actions on von Neumann algebras. Next we discuss some natural questions which remained open around $C_0$-dynamical systems. In particular we give examples of $C_0$- dynamical systems for groups acting properly on trees. Finally, we give a positive answer to the question of the ergodicity of such systems for non-periodic groups.
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