Phase transition in the Connes-Marcolli GL2-system
Operator Algebras
2007-10-18 v2 Dynamical Systems
Number Theory
Abstract
We develop a general framework for analyzing KMS-states on C*-algebras arising from actions of Hecke pairs. We then specialize to the system recently introduced by Connes and Marcolli and classify its KMS-states for inverse temperatures \beta\ne 0,1. In particular, we show that for each \beta\in(1,2] there exists a unique KMS_\beta-state.
Cite
@article{arxiv.math/0609315,
title = {Phase transition in the Connes-Marcolli GL2-system},
author = {Marcelo Laca and Nadia Larsen and Sergey Neshveyev},
journal= {arXiv preprint arXiv:math/0609315},
year = {2007}
}
Comments
23 pages; minor corrections, final version