Quantum complex projective spaces from Toeplitz cubes


Hajac P. M. , Kaygun A. , ZIELINSKI B.

JOURNAL OF NONCOMMUTATIVE GEOMETRY, vol.6, no.3, pp.603-621, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 3
  • Publication Date: 2012
  • Doi Number: 10.4171/jncg/100
  • Title of Journal : JOURNAL OF NONCOMMUTATIVE GEOMETRY
  • Page Numbers: pp.603-621

Abstract

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.