Primitive ideals and \(K\)-theoretic approach to Bost-Connes systems

DOI10.1016/j.aim.2016.08.005zbMath1359.46049arXiv1511.02662OpenAlexW2963211330MaRDI QIDQ317345

Takuya Takeishi

Publication date: 30 September 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.02662

zbMATH Keywords

\(C^*\)-algebra\(K\)-theorycrossed productprimitive idealBost-Connes system

Mathematics Subject Classification ID

Galois theory (11R32) (K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative dynamical systems (46L55) General theory of (C^*)-algebras (46L05) Zeta functions and (L)-functions of number fields (11R42) Adèle rings and groups (11R56) Classifications of (C^*)-algebras (46L35) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (3)

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 ⋮ Reconstructing the Bost-Connes semigroup actions from \(K\)-theory

Cites Work

• Unnamed Item
• Irreducible representations of Bost-Connes systems
• On \(K\)-theoretic invariants of semigroup \(C^*\)-algebras attached to number fields
• On Bost-Connes type systems for number fields
• A new characterization of arithmetic equivalence
• On arithmetic models and functoriality of Bost-Connes systems. With an appendix by Sergey Neshveyev

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