JournalsjncgVol. 1 , No. 4DOI 10.4171/jncg/12

Phase transition in the Connes–Marcolli GL<sub>2</sub>-system

  • Marcelo Laca

    University of Victoria, Canada
  • Nadia S. Larsen

    University of Oslo
  • Sergey Neshveyev

    University of Oslo
Phase transition in the Connes–Marcolli GL<sub>2</sub>-system cover

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.