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∗-alg...

Approximately finite (AF) C *-algebras are classified by approximately finite (r-discrete principal) groupoids. Certain natural triangular subalgebras of AF C *-algebras are similarly classified by triangular subsemigroupoids of AF groupoids [10]. Putting this in a more intuitive way, such subalgebras A are classified by the topologised fundamental binary relation R(A) induced on the Gelfand sp...