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

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.

28 pages. Section 2 and 4 are rewritten

References in corpus (3)

• Quantum Statistical Mechanics, L-series and Anabelian Geometry
• Reconstructing global fields from Dirichlet L-series
• Reconstructing global fields from dynamics in the abelianized Galois group

Cited by in corpus (2)

• Ground states of groupoid C*-algebras, phase transitions and arithmetic subalgebras for Hecke algebras
• $C^{\ast }$-algebras of right LCM monoids and their equilibrium states