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arxiv: 0907.1456 · v1 · submitted 2009-07-09 · 🧮 math.OA · math.DS

Von Neumann algebras arising from Bost-Connes type systems

Sergey Neshveyev This is my paper
classification 🧮 math.OA math.DS
keywords betatypebost-connesergodicitysystemsystemsactionactions
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We show that the KMS_beta-states of Bost-Connes type systems for number fields in the region 0<beta\le 1, as well as of the Connes-Marcolli GL_2-system for 1<beta\le 2, have type III_1. This is equivalent to ergodicity of various actions on adelic spaces. For example, the case beta=2 of the GL_2-system corresponds to ergodicity of the action of GL_2(Q) on Mat_2(A) with its Haar measure.

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