JournalsjncgVol. 7, No. 1pp. 291–300

The Bost–Connes phase transition and unitary representations

  • Tyrone Crisp

    Penn State, University Park, USA
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Abstract

We construct a family of unitary representations of the ax+bax+b group QQ+×\mathbb{Q}\rtimes\mathbb{Q}_+^\times. We show that this family of representations exhibits a “phase transition” analogous to that observed by Bost and Connes [2] and then explain how these representations are related to the equilibrium states of Bost and Connes.

Cite this article

Tyrone Crisp, The Bost–Connes phase transition and unitary representations. J. Noncommut. Geom. 7 (2013), no. 1, pp. 291–300

DOI 10.4171/JNCG/117