For finite directed acyclic graph R, C^*(F_R) is isomorphic to the AF core of C^*(E_R), with applications to quantum Grassmannians and flag manifolds.
Ellwood,A new characterisation of principal actions, Journal of Functional Analysis 173 (2000), 49–60
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On amplified graph C*-algebras as cores of Cuntz-Krieger algebras
For finite directed acyclic graph R, C^*(F_R) is isomorphic to the AF core of C^*(E_R), with applications to quantum Grassmannians and flag manifolds.