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Reconstructing the Bost--Connes semigroup actions from K-theory (1709.03281v2)
Published 11 Sep 2017 in math.OA and math.NT
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.