C*-algebras associated with integral domains and crossed products by actions on adele spaces

2009/06/26 by Joachim Cuntz, Xin Li, Cuntz, Joachim +1 · 3 citations
Mathematics · #11R04 #11R56 (Secondary) #46L05 #46L80 (Primary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #advanced mathematical theories #math.OA #msc:11R04 #msc:11R56 #msc:46L05 #msc:46L80

paper · pdf · doi:10.48550/arxiv.0906.4903

38 pages

arxiv created 2009/06/26 · openalex publication_date 2009/06/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the K-theory for C*-algebras naturally associated with rings of integers in number fields. The main ingredient is a duality theorem for arbitrary global fields. It allows us to identify the crossed product arising from affine transformations on the finite adeles with the analogous crossed product algebra over the infinite adele space.

Citations

• The Regular C*-algebra of an Integral Domain

Cited by

• Spectral Triples for Hensel-Steinitz Algebras
• K-Theory of Adelic and Rational Group C^*-algebras via Generalized Winding Numbers
• K-theory for ring C*-algebras attached to function fields

Related

• The cyclic homology and K-theory of certain adelic crossed products
• The Regular C*-algebra of an Integral Domain
• Crossed Product C^*-algebras Associated With p-adic Multiplication
• Classifying crossed product C*-algebras
• Partial crossed product description of the C*-algebras associated with integral domains