We complete the classification of Bost--Connes systems. We show that twoBost--Connes C*-algebras for number fields are isomorphic if and only if theoriginal semigroups actions are conjugate. Together with recent reconstructionresults in number theory by Cornelissen--de Smit--Li--Marcolli--Smit, weconclude that two Bost--Connes C*-algebras are isomorphic if and only if theoriginal number fields are isomorphic.
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机译:我们完成了Bost-Connes系统的分类。我们展示了Twobost - Connes C * -algeBras for Number字段是同构IfOmorphic且才有才能才有缀合的缀合物。与Cornelissen - De Smit - Li - Marcolli - SMIT的最近重建的重建事务所一起,WeConclude是两个Bost-Connes C * -algeBras是同性恋,如果才能才有,只有在理想数字段是同性的那样。
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