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

Tsuyoshi Kajiwara, Yasuo Watatani

    Research output: Contribution to journalArticlepeer-review


    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
    Issue number2
    Publication statusPublished - Mar 1 2011

    All Science Journal Classification (ASJC) codes

    • Algebra and Number Theory


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