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. (C) 2020 Elsevier Inc. All rights reserved.
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机译：我们完成了Bost-Connes系统的分类。 我们展示了两个Bost-Connes C * -algeBras for Number字段是同构IfOrphic，如果原始的半群动作是共轭。 与近期理论的最近的重建一起由Cornelissen-de Smit-Li-Marcolli-Smit一起，我们得出结论，如果原始数字字段是同构的，则两个Bost-Connes C * -algeBras是同性恋。 （c）2020 Elsevier Inc.保留所有权利。
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