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


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.

Cite this article

Marcelo Laca, Nadia S. Larsen, Sergey Neshveyev, Phase transition in the Connes–Marcolli GL<sub>2</sub>-system. J. Noncommut. Geom. 1 (2007), no. 4, pp. 397–430

DOI 10.4171/JNCG/12