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

Authors: Valentin Deaconu and Paul S. Muhly
Journal: Proc. Amer. Math. Soc. 129 (2001), 1077-1086
MSC (1991): Primary 46L55, 43A35; Secondary 43A07, 43A15, 43A22
Published electronically: October 4, 2000
MathSciNet review: 1814145
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Abstract: 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.

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Additional Information

Valentin Deaconu
Affiliation: Department of Mathematics, University of Nevada, Reno, Nevada 89557

Paul S. Muhly
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

Keywords: $C^{\ast}$-algebras, branched coverings, dynamical systems
Received by editor(s): June 30, 1999
Published electronically: October 4, 2000
Additional Notes: This research was supported in part by grants from the National Science Foundation.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

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