C^*-algebras associated with the ax+b-semigroup over \mathbb N

2006/11/17 by Joachim Cuntz, Cuntz, Joachim
Mathematics · #46L05 #58B34 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05 #msc:58B34

paper · pdf · doi:10.48550/arxiv.math/0611541

14 pages

arxiv created 2006/11/17 · openalex publication_date 2006/11/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a C^*-algebra which is naturally associated to the ax+b-semigroup over \mathbb N. It is simple and purely infinite and can be obtained from the algebra considered by Bost and Connes by adding one unitary generator which corresponds to addition. Its stabilization can be described as a crossed product of the algebra of continuous functions, vanishing at infinity, on the space of finite adeles for \mathbb Q by the natural action of the ax+b-group over \mathbb Q.

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• Semigroup C*-algebras of ax+b-semigroups
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