C^{\ast}-algebras associated with branched coverings

C^{\ast}-algebras associated with branched coverings

In this note we analyze the C^{\ast}-algebra associated with a branched covering both as a groupoid C^{\ast}-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 rela...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2001-04, Vol.129 (4), p.1077-1086
Hauptverfasser: Deaconu, Valentin, Muhly, Paul S.
Format: Artikel
Sprache:eng
Schlagworte:
Adjoints
Algebra
Equivalence relation
Homeomorphism
Inner products
Mathematical theorems
Operator theory
Quotients
Tensors
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Zusammenfassung:In this note we analyze the C^{\ast}-algebra associated with a branched covering both as a groupoid C^{\ast}-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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-00-05697-5