### 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 O_{p}(J) is simple and purely infinite.

Original language | English |
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Pages (from-to) | 427-449 |

Number of pages | 23 |

Journal | Journal of Operator Theory |

Volume | 65 |

Issue number | 2 |

Publication status | Published - Mar 1 2011 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Kajiwara, T., & Watatani, Y. (2011). C*-Algebras Associated With Algebraic Correspondences On The Riemann Sphere.

*Journal of Operator Theory*,*65*(2), 427-449.