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

Sergey Neshveyev
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Abstract

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

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Sergey Neshveyev. 2000-02-17. Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem. https://doi.org/10.1090/s0002-9939-02-06449-3

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