 

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 


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 CuntzKrieger
partial isometries which it contains iff it is invariant under the
gauge automorphisms. We study 1cocycles on the CuntzKrieger
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
ahopenwa@euler.math.ua.edu
Justin R. Peters:
Department of Mathematics, Iowa State University, Ames, IA 50011
peters@iastate.edu
Stephen C. Power:
Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.
s.power@lancaster.ac.uk

