### 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 |
---|---|

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 |

### Fingerprint

### 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.

**Hilbert C*-bimodules and continuous Cuntz-Krieger algebras.** / Kajiwara, Tsuyoshi; Watatani, Yasuo.

Research output: Contribution to journal › Article

*Journal of the Mathematical Society of Japan*, vol. 54, no. 1, pp. 35-59.

}

TY - JOUR

T1 - Hilbert C*-bimodules and continuous Cuntz-Krieger algebras

AU - Kajiwara, Tsuyoshi

AU - Watatani, Yasuo

PY - 2002

Y1 - 2002

N2 - 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 OX 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 OX 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.

AB - 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 OX 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 OX 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.

KW - C-algebras

KW - Hilbert C-bimodules

KW - K-theory

UR - http://www.scopus.com/inward/record.url?scp=0036069247&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036069247&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036069247

VL - 54

SP - 35

EP - 59

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 1

ER -