### Abstract

Results by Cuntz and Kreiger on uniqueness, simplicity and the ideal structure of the algebras O_{A} associated with finite matrices with entries in {0, 1} are generalized to the case where A is an infinite matrix whose rows and columns are eventually zero, but not identically zero. Similar results have been recently obtained by Kumjian, Pask, Raeburn and Renault from the viewpoint of Renault's theory of groupoids. An alternative approach, based on the realization of O_{A} as an algebra generated by a Hilbert C*-bimodule introduced by Pimsner, is proposed and compared.

Original language | English |
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Pages (from-to) | 3-18 |

Number of pages | 16 |

Journal | Journal of Operator Theory |

Volume | 45 |

Issue number | 1 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- Cuntz-Krieger algebra
- Hilbert bimodule

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Operator Theory*,

*45*(1), 3-18.

**Hilbert C*-bimodules and countably generated Cuntz-Krieger algebras.** / Kajiwara, Tsuyoshi; Pinzari, C.; Watatani, Y.

Research output: Contribution to journal › Article

*Journal of Operator Theory*, vol. 45, no. 1, pp. 3-18.

}

TY - JOUR

T1 - Hilbert C*-bimodules and countably generated Cuntz-Krieger algebras

AU - Kajiwara, Tsuyoshi

AU - Pinzari, C.

AU - Watatani, Y.

PY - 2001

Y1 - 2001

N2 - Results by Cuntz and Kreiger on uniqueness, simplicity and the ideal structure of the algebras OA associated with finite matrices with entries in {0, 1} are generalized to the case where A is an infinite matrix whose rows and columns are eventually zero, but not identically zero. Similar results have been recently obtained by Kumjian, Pask, Raeburn and Renault from the viewpoint of Renault's theory of groupoids. An alternative approach, based on the realization of OA as an algebra generated by a Hilbert C*-bimodule introduced by Pimsner, is proposed and compared.

AB - Results by Cuntz and Kreiger on uniqueness, simplicity and the ideal structure of the algebras OA associated with finite matrices with entries in {0, 1} are generalized to the case where A is an infinite matrix whose rows and columns are eventually zero, but not identically zero. Similar results have been recently obtained by Kumjian, Pask, Raeburn and Renault from the viewpoint of Renault's theory of groupoids. An alternative approach, based on the realization of OA as an algebra generated by a Hilbert C*-bimodule introduced by Pimsner, is proposed and compared.

KW - Cuntz-Krieger algebra

KW - Hilbert bimodule

UR - http://www.scopus.com/inward/record.url?scp=0040956500&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040956500&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040956500

VL - 45

SP - 3

EP - 18

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 0379-4024

IS - 1

ER -