Phase transitions on Hecke C*-algebras and class-field theory over ℚ

DOI10.1515/CRELLE.2006.043zbMath1136.11070arXivmath/0410305MaRDI QIDQ5479402

Marcelo Laca, Machiel van Frankenhuijsen

Publication date: 7 July 2006

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410305

zbMATH Keywords

dynamical systemclass-field theoryHecke \(C^*\)-algebra

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) General theory of (C^*)-algebras (46L05) Class field theory (11R37) Hecke-Petersson operators, differential operators (one variable) (11F25)

Related Items (12)

KMS states on a generalized Toeplitz algebra ⋮ Hecke algebras from groups acting on trees and HNN extensions. ⋮ Hecke algebras of semidirect products ⋮ \(C^*\)-algebras of Toeplitz type associated with algebraic number fields ⋮ Constructing number field isomorphisms from \(*\)-isomorphisms of certain crossed product \(\mathrm{C}^*\)-algebras ⋮ 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 ⋮ Hecke algebras for protonormal subgroups. ⋮ Phase transition on the Toeplitz algebra of the affine semigroup over the natural numbers ⋮ Bost-Connes type systems for function fields ⋮ On Bost-Connes type systems for number fields ⋮ Partial crossed product description of the 𝐶*-algebras associated with integral domains

Cites Work

• Spectra of Liouville operators
• Induced factor representations of discrete groups and their types
• Semigroups of *-endomorphisms, Dirichlet series, and phase transitions
• Semigroup crossed products and the Toeplitz algebras of nonabelian groups
• A Semigroup Crossed Product Arising in Number Theory
• From Endomorphisms to Automorphisms and Back: Dilations and Full Corners
• Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem
• Hecke algebras of semidirect products
• Hecke Algebras of Group Extensions

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