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Subalgebras of groupoid C*-algebras.

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

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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
Journal or Publication Title: The 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: 09 Oct 2013 13:12
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19382

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