### Abstract

Pimsner introduced the C*-algebra O_{X}generated by a Hilbert bimoduleXover a C*-algebra A. We look for additional conditions thatXshould satisfy in order to study the simplicity and, more generally, the ideal structure of O_{X}whenXis finite projective. We introduce two conditions, "(I)-freeness" and "(II)-freeness," stronger than the former, in analogy with J. Cuntz and W. Krieger (Invent. Math.56, 1980, 251-268) and J. Cuntz (Invent. Math.63, 1981, 25-40), respectively. (I)-freeness comprehends the case of the bimodules associated with an inclusion of simple C*-algebras with finite index, real or pseudoreal bimodules with finite intrinsic dimension, and the case of "Cuntz-Krieger bimodules." IfXsatisfies this condition the C*-algebra O_{X}does not depend on the choice of the generators when A is faithfully represented. As a consequence, ifXis (I)-free and A isX-simple, then O_{X}is simple. In the case of Cuntz-Krieger algebras O_{A},X-simplicity corresponds to the irreducibility of the matrix A. If A is simple and p.i. then O_{X}is p.i.; if A is nonnuclear then O_{X}is nonnuclear. Thus we provide many examples of (purely) infinite nonnuclear simple C*-algebras. Furthermore ifXis (II)-free, we determine the ideal structure of O_{X}.

Original language | English |
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Pages (from-to) | 295-322 |

Number of pages | 28 |

Journal | Journal of Functional Analysis |

Volume | 159 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 10 1998 |

### All Science Journal Classification (ASJC) codes

- Analysis

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## Cite this

*Journal of Functional Analysis*,

*159*(2), 295-322. https://doi.org/10.1006/jfan.1998.3306