论文标题
构建数字字段同构，来自某些交叉产品C * - 代理的 * - 异态性
Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras
论文作者
论文摘要
我们证明，在有限的Adeles环上，与数字的乘法组的作用相关的交叉产物C* - 代数在以下明确的意义上是刚性的：给定两个这样的C* - 代数之间的任何* - 异态性，我们在下层数字之间构建一个同构。作为应用程序，我们使用拓扑完整组证明了Neukirch-uchida定理的类似物，该组提供了与数字字段相关联的新的离散组，其抽象同构类完全表征了数字字段。
We prove that the class of crossed product C*-algebras associated with the action of the multiplicative group of a number field on its ring of finite adeles is rigid in the following explicit sense: Given any *-isomorphism between two such C*-algebras, we construct an isomorphism between the underlying number fields. As an application, we prove an analogue of the Neukirch--Uchida theorem using topological full groups, which gives a new class of discrete groups associated with number fields whose abstract isomorphism class completely characterises the number field.
