Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Subalgebras of groupoid C*-algebras.
AU - Power, S. C.
AU - Hopenwasser, A.
AU - Peters, J.
PY - 2005
Y1 - 2005
N2 - 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.
AB - 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.
KW - Graph C algebras
KW - triangular algebras
KW - nest algebras
KW - spectral theorem for bimodules
KW - groupoids
KW - cocycles
M3 - Journal article
VL - 11
SP - 351
EP - 386
JO - New York Journal of Mathematics
JF - New York Journal of Mathematics
SN - 1076-9803
ER -