Limit C*-algebras associated with an automorphism

2003/12/03 by Baruch Solel, Solel, Baruch
Mathematics · #46L05 #46L35 #46L40 #46L80 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.OA #msc:46L05 #msc:46L35 #msc:46L40 #msc:46L80

paper · pdf · doi:10.48550/arxiv.math/0312089

Latex file, To appear in Math. Scand

arxiv created 2003/12/03 · openalex publication_date 2003/12/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present and study C*-algebras generated by "periodic weighted creation operators" on the Fock space associated with an automorphism α on a C*-algebra A. These algebras can be viewed as generalized Bunce-Deddens algebras associated with the automorphism and can be written as a certain direct limit. We prove a crossed product presentation for such an algebra and find a necessary and sufficient condition for it to be simple. In the case where the automorphism is induced by an irrational rotation (on C(\mathbbT)) we compute the K-theory groups and obtain a complete classification of these algebras.

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