Subalgebras of groupoid C*-algebras.

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

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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.

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Journal Article
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New York Journal of Mathematics
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19 Nov 2008 16:33
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22 Feb 2021 00:48