C*-algebras associated with branched coverings

2001/03/27 by Valentin Deaconu, Paul S. Muhly · 1 citation
Mathematics · #math.OA #msc:46L55 #msc:43A07 #msc:43A15 #msc:43A22

paper · pdf

published as Proceedings of the AMS vol 129 No. 4 (2000) pp 1077-1086

arxiv created 2001/03/27 · arxiv updated 2009/11/30

Abstract

In this note we analyze the C*-algebra associated with a branched covering both as a groupoid C*-algebra and as a Cuntz-Pimsner algebra. We determine conditions when the algebra is simple and purely infinite. We indicate how to compute the K-theory of several examples, including one related to rational maps on the Riemann sphere.

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• On morphisms of topological quivers

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• C*-algebras of commuting endomorphisms
• Groupoids and C*-algebras for categories of paths
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• Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences