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

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

2000-02-17

arxiv.org/abs/math/0002141v1

Mathematics

Operator Algebras

LaTeX2e, 4 pages

Scientific paper

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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