Phase transition in the Connes–Marcolli -system
Marcelo Laca
University of Victoria, CanadaNadia S. Larsen
University of OsloSergey Neshveyev
University of Oslo
![Phase transition in the Connes–Marcolli $\mathrm{GL}_2$-system cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jncg-volume-1-issue-4.png&w=3840&q=90)
Abstract
We develop a general framework for analyzing KMS-states on -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 . In particular, we show that for each there exists a unique KMS-state.
Cite this article
Marcelo Laca, Nadia S. Larsen, Sergey Neshveyev, Phase transition in the Connes–Marcolli -system. J. Noncommut. Geom. 1 (2007), no. 4, pp. 397–430
DOI 10.4171/JNCG/12