The $C^*$-algebras of quantum lens and weighted projective spaces - Tomasz Brzezinski (Journal of Noncommutative Geometry, 2018)
It is shown that the algebra of continuous functions on the quantum 2n+1-dimensional lens space C(L2n+1q(N;m0,…,mn)) is a graph C*-algebra, for arbitrary positive weights m0,…,mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of continuous functions on the quantum sphere S2n+1q and the cyclic group ℤN, with the labelling induced by the weights. Based on this description, the K-groups of specific examples are computed. Furthermore, the K-groups of the algebras of continuous functions on quantum weighted projective spaces C(ℙnq(m0,…,mn)), interpreted as fixed points under the circle action on C(S2n+1q), are computed under a mild assumption on the weights.