论文标题
一般统一的ROE代数刚度
General uniform Roe algebra rigidity
论文作者
论文摘要
我们将均匀ROE代数刚度的所有已知结果推广到任意局部有限的粗空间的设置。例如，我们表明，均匀局部有限的粗空间的均匀的ROE代数之间的同构，其均匀的Roe代数仅包含紧凑的幽灵投影，这意味着基本空间是高度等效的。此外，如果其中一个空间具有属性A，则基本空间在肉类上是相当于的。我们还为在基础空间方面存在嵌入到遗传下的亚词架上的表征。作为一种应用，我们部分回答了关于统一的Roe代数的cartan子代数的白色和威利特的问题。
We generalize all known results on rigidity of uniform Roe algebras to the setting of arbitrary uniformly locally finite coarse spaces. For instance, we show that isomorphism between uniform Roe algebras of uniformly locally finite coarse spaces whose uniform Roe algebras contain only compact ghost projections implies that the base spaces are coarsely equivalent. Moreover, if one of the spaces has property A, then the base spaces are bijectively coarsely equivalent. We also provide a characterization for the existence of an embedding onto hereditary subalgebra in terms of the underlying spaces. As an application, we partially answer a question of White and Willett about Cartan subalgebras of uniform Roe algebras.
