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Phase transition in the Connes-Marcolli GL2-system

Marcelo Laca·Nadia Larsen·Sergey Neshveyev
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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\ne 0,1. In particular, we show that for each β\in(1,2] there exists a unique KMS_β-state.

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Marcelo Laca, Nadia Larsen, Sergey Neshveyev. 2007-10-18. Phase transition in the Connes-Marcolli GL2-system. https://doi.org/10.4171/jncg%2F12

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