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arXiv · 1709.03281

Reconstructing the Bost--Connes semigroup actions from K-theory

Yosuke Kubota·Takuya Takeishi
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Abstract

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.

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Yosuke Kubota, Takuya Takeishi. 2017-09-11. Reconstructing the Bost--Connes semigroup actions from K-theory. https://arxiv.org/abs/1709.03281

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