论文标题
在与一个数字字段的完整Adele环相关的C* - 代数上
On the C*-algebra associated with the full adele ring of a number field
论文作者
论文摘要
一个数字的乘法组通过在该场的完整Adele环上乘法起作用。概括了LACA和Raeburn的定理，我们明确描述了与此动作相关的交叉产物C* - 代数的原始理想空间。然后，我们使用K理论不变性区分数字字段的真实，复杂和有限的位置。将这些结果与作者最近的刚性定理相结合，这意味着两个这样的C * - 代数之间的任何 *异态性都会引起基础数字字段的同构，这些字段是由 * - 异构形态构成的。
The multiplicative group of a number field acts by multiplication on the full adele ring of the field. Generalising a theorem of Laca and Raeburn, we explicitly describe the primitive ideal space of the crossed product C*-algebra associated with this action. We then distinguish real, complex, and finite places of the number field using K-theoretic invariants. Combining these results with a recent rigidity theorem of the authors implies that any *-isomorphism between two such C*-algebras gives rise to an isomorphism of the underlying number fields that is constructed from the *-isomorphism.
