Power, S. C. and Hopenwasser, A. and Peters, J. (2005) *Subalgebras of groupoid C*-algebras.* New York Journal of Mathematics, 11. pp. 351-386. ISSN 1076-9803

## Abstract

We prove a spectral theorem for bimodules in the context of graph C*-algebras. A bimodule over a suitable abelian algebra is determined by its spectrum (i.e., its groupoid partial order) iff it is generated by the Cuntz-Krieger partial isometries which it contains iff it is invariant under the gauge automorphisms. We study 1-cocycles on the Cuntz-Krieger groupoid associated with a graph C*-algebra, obtaining results on when integer valued or bounded cocycles on the natural AF subgroupoid extend. To a finite graph with a total order, we associate a nest subalgebra of the graph C*-algebra and then determine its spectrum. This is used to investigate properties of the nest subalgebra. We give a characterization of the partial isometries in a graph C*-algebra which normalize a natural diagonal subalgebra and use this to show that gauge invariant generating triangular subalgebras are classified by their spectra.

Item Type: | Article |
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Journal or Publication Title: | New York Journal of Mathematics |

Uncontrolled Keywords: | Graph C* algebras ; triangular algebras ; nest algebras ; spectral theorem for bimodules ; groupoids ; cocycles |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 19382 |

Deposited By: | ep_ss_importer |

Deposited On: | 19 Nov 2008 16:33 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 05 Feb 2016 00:01 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19382 |

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