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- W223829843 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." @default.
- W223829843 created "2016-06-24" @default.
- W223829843 date "1989-12-01" @default.
- W223829843 modified "2023-10-13" @default.
- W223829843 title "Subalgebras of groupoid C*-algebras." @default.
- W223829843 doi "https://doi.org/10.1515/crll.1989.402.41" @default.
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