### Abstract

Let (G, P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules in the sense of Fowler. Under mild hypotheses we associate to X a C^{*}-algebra which we call the Cuntz-Nica-Pimsner algebra of X. Our construction generalises a number of others: a sub-class of Fowler's Cuntz-Pimsner algebras for product systems of Hilbert bimodules; Katsura's formulation of Cuntz-Pimsner algebras of Hilbert bimodules; the C^{*}-algebras of finitely aligned higher-rank graphs; and Crisp and Laca's boundary quotients of Toeplitz algebras. We show that for a large class of product systems X, the universal representation of X in its Cuntz-Nica-Pimsner algebra is isometric.

Original language | English |
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Pages (from-to) | 349-376 |

Number of pages | 28 |

Journal | Journal of Operator Theory |

Volume | 64 |

Issue number | 2 |

Publication status | Published - Sep 2010 |

Externally published | Yes |

### Keywords

- Cuntz-pimsner algebra
- Hilbert bimodule

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## Cite this

^{*}-algebras associated to product systems of Hilbert bimodules.

*Journal of Operator Theory*,

*64*(2), 349-376.