Phase transition in the Connes-Marcolli \(\mathrm{GL}_2\)-system

DOI10.4171/JNCG/12zbMath1143.46039arXivmath/0609315OpenAlexW2162549597MaRDI QIDQ2472578

Marcelo Laca, Nadia S. Larsen, Sergey V. Neshveyev

Publication date: 22 February 2008

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609315

zbMATH Keywords

KMS-statesHecke pairs

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Noncommutative dynamical systems (46L55) Quantum equilibrium statistical mechanics (general) (82B10) Noncommutative geometry (à la Connes) (58B34)

Related Items

Hypergroupoids and \(C^\ast\)-algebras ⋮ The Riemann–Roch strategy ⋮ Ground states of groupoid \(C^\ast\)-algebras, phase transitions and arithmetic subalgebras for Hecke algebras ⋮ Hecke algebras of semidirect products and the finite part of the Connes-Marcolli \(C^*\)-algebra ⋮ Crossed Products by Hecke Pairs ⋮ Type III\(_{1}\) equilibrium states of the Toeplitz algebra of the affine semigroup over the natural numbers ⋮ Phase transition on the Toeplitz algebra of the affine semigroup over the natural numbers ⋮ On Bost-Connes type systems for number fields ⋮ On the countable measure-preserving relation induced on a homogeneous quotient by the action of a discrete group ⋮ Noncommutative geometry of groups like \(\Gamma_0(N)\)

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