Quantum complex projective spaces from Toeplitz cubes

  • Piotr M. Hajac

    IMPAN, Warsaw, Poland
  • Atabey Kaygun

    Bahçeşehir University, Istanbul, Turkey
  • Bartosz Zieliński

    University of Lodz, Poland


From NN-tensor powers of the Toeplitz algebra, we construct a multi-pullback C*-algebra that is a noncommutative deformation of the complex projective space PN ⁣(C)\mathbb{P}^N\!(\mathbb{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.

Cite this article

Piotr M. Hajac, Atabey Kaygun, Bartosz Zieliński, Quantum complex projective spaces from Toeplitz cubes. J. Noncommut. Geom. 6 (2012), no. 3, pp. 603–621

DOI 10.4171/JNCG/100