论文标题
组von Neumann代数，内部休闲性和连续环的单位组
Group von Neumann algebras, inner amenability, and unit groups of continuous rings
论文作者
论文摘要
我们证明，如果一个离散的$ g $不可内在的amen依，那么与$ g $的von Neumann代数相关的操作环的单位组对于其等级度量所产生的拓扑而言是不合同的。这提供了非差异不可约合的连续环（在冯·诺伊曼的意义上）的示例，其单位群在等级拓扑方面是不可能的。我们的论点建立并使用了与eymard的连接 - greenleaf的舒适性在$ \ mathrm {ii} _ {1} $ action the the Unive triventions的相关空间上的统一组的动作。
We prove that, if a discrete group $G$ is not inner amenable, then the unit group of the ring of operators affiliated with the group von Neumann algebra of $G$ is non-amenable with respect to the topology generated by its rank metric. This provides examples of non-discrete irreducible, continuous rings (in von Neumann's sense) whose unit groups are non-amenable with regard to the rank topology. Our argument establishes and uses connections with Eymard--Greenleaf amenability of the action of the unitary group of a $\mathrm{II}_{1}$ factor on the associated space of projections of a fixed trace.
