Phase transition in the Connes–Marcolli $\mathrm{GL}_2$-system

Marcelo Laca; Nadia S. Larsen; Sergey Neshveyev

doi:10.4171/jncg/12

JournalsjncgVol. 1, No. 4pp. 397–430

Phase transition in the Connes–Marcolli $GL_{2}$ -system

Marcelo Laca
University of Victoria, Canada
Nadia S. Larsen
University of Oslo
Sergey Neshveyev
University of Oslo

$Phase transition in the Connes–Marcolli $\mathrm{GL}_2$-system cover$

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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 $β \neq = 0, 1$ . In particular, we show that for each $β \in (1, 2]$ there exists a unique KMS $_{β}$ -state.

Cite this article

Marcelo Laca, Nadia S. Larsen, Sergey Neshveyev, Phase transition in the Connes–Marcolli $GL_{2}$ -system. J. Noncommut. Geom. 1 (2007), no. 4, pp. 397–430

DOI 10.4171/JNCG/12