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.
Rudnik,The K-theory of the triple-Toeplitz deformation of the complex projective plane, Banach Center Pub
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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.