Reconstructing the Bost--Connes semigroup actions from K-theory
Reconstructing the Bost--Connes semigroup actions from K-theory
复制标题
从K理论重构Bost--Connes半群作用
DOI：
10.1016/j.aim.2020.107070
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发表时间：
2020
影响因子：
1.7
通讯作者：
Takeishi Takuya
中科院分区：
文献类型：
--
作者：
Kubota Yosuke;Takeishi Takuya
我们完成了Bost-Connes系统的分类。证明了数域上的两个Bost-Connes C*-代数同构的充要条件是原半群作用是共轭的。结合最近Cornelissen-de Smit-Li-Marcoli-Smit在数论中的重构结果，我们得出结论：两个Bost-Connes C*-代数同构的充要条件是原数域同构。
We complete the classification of Bost–Connes systems. We show that two Bost–Connes C*-algebras for number fields are isomorphic if and only if the original semigroups actions are conjugate. Together with recent reconstruction results in number theory by Cornelissen–de Smit–Li–Marcolli–Smit, we conclude that two Bost–Connes C*-algebras are isomorphic if and only if the original number fields are isomorphic.