The center of some quantum projective planes (Q1270981)

Let \(A\) be a homogeneous coordinate ring of a quantum projective plane, which is a non-commutative analogue of the polynomial ring in three variables. When \(A\) is a finite module over its center \(Z(A)\), the author defines a scheme \(S=\text{Proj}(Z(A))\) and a sheaf \(\mathcal A\) of \({\mathcal O}_S\)-algebras by \({\mathcal A}(S_{(f)})=A[f^{-1}]\), where \(S_{(f)}\) is the open affine subset of \(S\) for each non-zero homogeneous element \(f\in Z(A)\). The center \(\mathcal Z\) of \(\mathcal A\) is defined by \({\mathcal Z}(S_{(f)})=Z(A[f^{-1}]_0)\) and \(\text{Spec}({\mathcal Z})\) is computed for several families of algebras \(A\).