论文标题
具有属性A的粗制度空间的Gelfand型二元性A
A Gelfand-type duality for coarse metric spaces with property A
论文作者
论文摘要
我们证明了具有Yu的财产a的给定局部有限的度量空间的以下两个结果a： 1）其均匀的ROE代数的外部自动形态群对其一组族裔粗糙等效度模态近似值。 2）其ROE代数的外部自动形态群对其粗糙等价模型的亲密度是同构的。 主要困难在于后者。为了证明，我们为ROE代数之间的地图获得了几个均匀的近似性结果，并使用它们来获得有关ROE代数的Cartan Masas的定理。我们将上述结果的多个应用程序应用于混凝土度量空间。
We prove the following two results for a given uniformly locally finite metric space with Yu's property A: 1) The group of outer automorphisms of its uniform Roe algebra is isomorphic to its group of bijective coarse equivalences modulo closeness. 2) The group of outer automorphisms of its Roe algebra is isomorphic to its group of coarse equivalences modulo closeness. The main difficulty lies in the latter. To prove that, we obtain several uniform approximability results for maps between Roe algebras and use them to obtain a theorem about the `uniqueness' of Cartan masas of Roe algebras. We finish the paper with several applications of the results above to concrete metric spaces.
