Phase transition in the Connes-Marcolli GL2-system
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.
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