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Cuntz—Krieger algebras associated with Fuchsian groups

Published online by Cambridge University Press:  19 September 2008

J. S. Spielberg
J. S. Spielberg
Affiliation:
Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA
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Abstract

For Fuchsian groups of the first kind containing parabolic elements, it is shown that the action on a suitable disconnection of the limit circle generates a Cuntz—Krieger C*-algebra. This clarifies and generalizes the situation of the subalgebra within O2, and provides a new proof of the simplicity and nuclearity of certain Cuntz—Krieger algebras. The proof relies on the Markov partition obtained from a suitable fundamental polygon for the group. Counter examples are given if an unsuitable fundamental polygon is used.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 3 , September 1993 , pp. 581 - 595
Copyright
Copyright © Cambridge University Press 1993

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