Reconstructing the Bost--Connes semigroup actions from K-theory
Operator Algebras
2018-07-16 v2 Number 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.
Keywords
Cite
@article{arxiv.1709.03281,
title = {Reconstructing the Bost--Connes semigroup actions from K-theory},
author = {Yosuke Kubota and Takuya Takeishi},
journal= {arXiv preprint arXiv:1709.03281},
year = {2018}
}
Comments
28 pages. Section 2 and 4 are rewritten