belongs to this class if and only if the corresponding coordinate algebra has a set of generators with length no greater than 2.

We next generalize some of the results of [@DL10] to ${\mathbb{P}}_q({\underline}{\ell})$. After an interlude on irreducible representations in §\[sec:irreps\], we construct a family of $1$-summable Fredholm modules in §\[sec:Khom\], and a class of Dirac operators (and then spectral triples) in §\[sec:otto\].

In §\[sec:sei\], a quantum weighted projective space ${\mathbb{P}}_q({\underline}{\ell})$ is shown to be the base space of a quantum principal circle bundle whose total space is a quantum lens space $L_q(p;{\underline}{\ell})$, with explicit examples in §\[sec:sette\]. For the weighted projective lines this was done in [@BF12] and in generality in [@AKL14].

In §\[sec:nove\], we construct projections in the $C^*$-algebra of quantum weighted projective spaces and prove that the Fredholm modules of §\[sec:Khom\] are linearly independent in K-homology.

We finish by mentioning possible uses of quantum projective lines (and more general quantum projective spaces) for Chern-Simons theories. These theories were generalised in [@BT13] to circle-bundles over orbifolds (such as weighted projective spaces). However, these applications go beyond the scope of the present paper and should await a future time.

*General notations.* By a *$*$-algebra* we mean a complex 