Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem

Neshveyev, Sergey

Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem

Authors

Description

For each β\in(0,+\infty) there exists a canonical measure μ_βon the ring A_f of finite adeles. We show that the positive rationals act ergodically on (A_f,μ_β) for β\in(0,1], and then deduce from this the uniqueness of KMS_β-states for the Bost-Connes system.
LaTeX2e, 4 pages