Quantum complex projective spaces from Toeplitz cubes

摘要

From N-tensor powers of the Toeplitz algebra, we construct a multi-pullback C*-algebra that is a noncommutative deformation of the complex projective space P ~N(C). 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.