Notes on quantum weighted projective spaces and multidimensional teardrops

It is shown that the coordinate algebra of the quantum 2n+1-dimensional lens space O(Lq2n+1(∏i=0nmi;m0,…,mn)) is a principal CZ-comodule algebra or the coordinate algebra of a circle principal bundle over the weighted quantum projective space WPqn(m0,…,mn). Furthermore, the weighted U(1)-action or the CZ-coaction on the quantum odd dimensional sphere algebra O(Sq2n+1) that defines WPqn(1,m1,…,mn) is free or principal. Analogous results are proven for quantum real weighted projective spaces RPq2n(m0,…,mn). The K-groups of WPqn(1,…,1,m) and RPq2n(1,…,1,m) and the K1-group of Lq2n+1(N;m0,…,mn) are computed.