Quantum lens spaces and principal actions on graph C*-algebras

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We study certain principal actions on noncommutative C*-algebras. Our main examples are the Zₚ- and T-actions on the odd-dimensional quantum spheres, yielding as fixed-point algebras quantum lens spaces and quantum complex projective spaces, respectively. The key tool in our analysis is the relation of the ambient C*-algebras with the Cuntz-Krieger algebras of directed graphs. A general result about the principality of the gauge action on graph algebras is given.