### Abstract

We consider certain correspondences on disjoint unions Ω of circles which naturally give Hilbert C^{*}-bimodules X over circle algebras A. The bimodules X generate C^{*}-algebras O_{X} which are isomorphic to a continuous version of Cuntz-Krieger algebras introduced by Deaconu using groupoid method. We study the simplicity and the ideal structure of the algebras under some conditions using (I)-freeness and (II)-freeness previously discussed by the authors. More precisely, we have a bijective correspondence between the set of closed two sided ideals of O_{X} and saturated hereditary open subsets of Ω. We also note that a formula of K-groups given by Deaconu is given without any minimality condition by just applying Pimsner's result.

Original language | English |
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Pages (from-to) | 35-59 |

Number of pages | 25 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 54 |

Issue number | 1 |

Publication status | Published - 2002 |

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### Keywords

- C-algebras
- Hilbert C-bimodules
- K-theory

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the Mathematical Society of Japan*,

*54*(1), 35-59.