Von Neumann algebras arising from Bost-Connes type systems
Operator Algebras
2009-07-10 v1 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.0907.1456,
title = {Von Neumann algebras arising from Bost-Connes type systems},
author = {Sergey Neshveyev},
journal= {arXiv preprint arXiv:0907.1456},
year = {2009}
}
Comments
AMS-LaTeX, 12 pages