On Bost-Connes type systems for number fields

Abstract

We give a complete description of the phase transition of the Bost-Connes type systems for number fields recently introduced by Connes-Marcolli-Ramachandran and Ha-Paugam. We also introduce a notion of K-lattices and discuss an interpretation of these systems in terms of 1-dimensional K-lattices.

12 pages; small corrections, references added

References in corpus (4)

• From Physics to Number Theory via Noncommutative Geometry. Part I: Quantum Statistical Mechanics of Q-lattices
• Phase transition in the Connes-Marcolli GL2-system
• Phase transitions on Hecke C*-algebras and class-field theory over Q
• Hecke algebras of semidirect products and the finite part of the Connes-Marcolli C*-algebra

Cited by in corpus (18)

• KMS states on the C*-algebras of non-principal groupoids
• Type III_1 equilibrium states of the Toeplitz algebra of the affine semigroup over the natural numbers
• On stochastic generation of ultrametrics in high-dimension Euclidean spaces
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• C*-algebras from actions of congruence monoids on rings of algebraic integers
• Von Neumann algebras arising from Bost-Connes type systems
• Ground states of groupoid C*-algebras, phase transitions and arithmetic subalgebras for Hecke algebras
• KMS states on Nica-Toeplitz C*-algebras
• Quantum Statistical Mechanics of the Absolute Galois Group
• Traces on crossed products
• Phase transitions on C*-algebras from actions of congruence monoids on rings of algebraic integers
• Quantum statistical mechanics in arithmetic topology
• The ideal intersection property for essential groupoid C*-algebras
• Endomotives of toric varieties
• Partition functions as C*-dynamical invariants and actions of congruence monoids
• Ergodicity of the action of K* on A_K
• AF $C^{\ast }$-algebras from non AF groupoids
• Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras