On K-theoretic invariants of semigroup C*-algebras attached to number fields

2012/12/13 by Xin Li, Li, Xin
Computer Science · Mathematics · #46L80 #Advanced Algebra and Logic #Advanced Operator Algebra Research #FOS: Mathematics #Functional Equations Stability Results #Number Theory (math.NT) #Operator Algebras (math.OA) #Primary 46L05 #Secondary 11Rxx

paper · pdf · doi:10.48550/arxiv.1212.3199

openalex publication_date 2012/12/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that semigroup C*-algebras attached to ax+b-semigroups over rings of integers determine number fields up to arithmetic equivalence, under the assumption that the number fields have the same number of roots of unity. For finite Galois extensions, this means that the semigroup C*-algebras are isomorphic if and only if the number fields are isomorphic.

Citations

• Nuclearity of semigroup C*-algebras and the connection to amenability
• On the K-theory of crossed products by automorphic semigroup actions

Related

• On K-theoretic invariants of semigroup C*-algebras attached to number fields, Part II
• Semigroup C*-algebras of ax+b-semigroups
• Semigroup C*-algebras and amenability of semigroups
• Reconstructing the Bost--Connes semigroup actions from K-theory
• A remark on invariants for C*-algebras of stable rank one