K-theory for ring C*-algebras attached to function fields

2009/11/26 by Joachim Cuntz, Xin Li, Cuntz, Joachim +1
Mathematics · #14H05 (Secondary) #46L05 #46L80 (Primary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA #msc:14H05 #msc:46L05 #msc:46L80

paper · pdf · doi:10.48550/arxiv.0911.5023

19 pages

arxiv created 2009/11/26 · openalex publication_date 2009/11/26 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the K-theory of ring C*-algebras for polynomial rings over finite fields. The key ingredient is a duality theorem which we had obtained in a previous paper. It allows us to show that the K-theory of these algebras has a ring structure and to determine explicit generators. Our main result also reveals striking similarities between the number field case and the function field case.

Citations

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

Related

• K-theory for ring C*-algebras attached to function fields with only one infinite place
• Ring C*-algebras
• C*-algebras associated with integral domains and crossed products by actions on adele spaces
• The K-theory of the C*-algebras associated to rational functions
• A kind of KK-theory for rings