C*-Algebras Associated With Algebraic Correspondences On The Riemann Sphere

Tsuyoshi Kajiwara, Yasuo Watatani

Research output: Contribution to journalArticle

Abstract

Let p(z,w) be a polynomial in two variables. We call the solution of the algebraic equation p(z,w) = 0 an algebraic correspondence. We regard it as the graph of the multivalued function z → w defined implicitly by p(z,w) = 0. Algebraic correspondences on the Riemann sphere C{double struck}̂ generalize both Kleinian groups and rational functions. We introduce C*-algebras associated with algebraic correspondences on the Riemann sphere. We show that if an algebraic correspondence is free and expansive on a closed p-invariant subset J of C{double-struck}̂, then the associated C*-algebra Op(J) is simple and purely infinite.

Original languageEnglish
Pages (from-to)427-449
Number of pages23
JournalJournal of Operator Theory
Volume65
Issue number2
Publication statusPublished - Mar 1 2011

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Keywords

  • Algebraic correspondence
  • Complex dynamical system
  • Hilbert C*-bimodule
  • Purely infinite C*-algebra

ASJC Scopus subject areas

  • Algebra and Number Theory

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