From -tensor powers of the Toeplitz algebra, we construct a multi-pullback C*-algebra that is a noncommutative deformation of the complex projective space . Using Birkhoff’s Representation Theorem, we prove that the lattice of kernels of the canonical projections on components of the multi-pullback C*-algebra is free. This shows that our deformation preserves the freeness of the lattice of subsets generated by the affine covering of the complex projective space.
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Piotr M. Hajac, Atabey Kaygun, Bartosz Zieliński, Quantum complex projective spaces from Toeplitz cubes. J. Noncommut. Geom. 6 (2012), no. 3, pp. 603–621DOI 10.4171/JNCG/100