Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem
Sergey Neshveyev
Abstract
For each β∈(0,+∞) there exists a canonical measure μβon the ring Af of finite adeles. We show that the positive rationals act ergodically on (Af,μβ) for β∈(0,1], and then deduce from this the uniqueness of KMSβ-states for the Bost-Connes system.
Create a lesson
Related papers
The generator problem for C*-algebras with comparison
Ben Bouwen, Jorge Castillejos, Jakub Curda
Actions of Fell bundles, II: tensor products and Fourier-Stieltjes algebras
Erik Bédos, Roberto Conti
A note on purely infinite extensions
Ping Wong Ng, Cangyuan Wang
Wiener's lemma for quasicrystals: hull-uniform decay of covariant kernels on Delone sets
Diego Jaure
Homotopies of constant Cuntz classes in pure C*-algebras
Chrisil Ouseph, Andrew S. Toms
Mean dimension and radius of comparison
George A. Elliott, Zhuang Niu