New York Journal of Mathematics
Volume 11 (2005) 351-386


Alan Hopenwasser, Justin R. Peters, and Stephen C. Power

Subalgebras of graph C* algebras

Published: August 26, 2005
Keywords: Graph C* algebras, triangular algebras, nest algebras, spectral theorem for bimodules, groupoids, cocycles
Subject: 47L40

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.

Author information

Alan Hopenwasser:
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487

Justin R. Peters:
Department of Mathematics, Iowa State University, Ames, IA 50011

Stephen C. Power:
Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.