Phase transition in the connes-marcolli GL2-system

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 β ≠ 0, 1. In particular, we show that for each β ∈ (1, 2] there exists a unique KMSβ-state. © 2013 EMS Publishing House.