Phase transition in the Connes-Marcolli GL2-system

2006/09/11 by Laca, Marcelo, Larsen, Nadia, Neshveyev, Sergey
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.math/0609315

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 KMS_β-state.

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