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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58712For 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 pagesOperator Algebras46L55Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theoremtext