Cuntz-Krieger algebras associated with Fuchsian groups

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13 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)581-595
Number of pages15
JournalErgodic Theory and Dynamical Systems
Volume13
Issue number3
DOIs
StatePublished - Sep 1993

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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