Quantum projective space from Toeplitz cubes
Quantum Algebra
2010-08-05 v1 Operator Algebras
Abstract
From N-tensor powers of the Toeplitz algebra, we construct a multipullback C*-algebra that is a noncommutative deformation of the complex projective space CP(N). Using Birkhoff's Representation Theorem, we prove that the lattice of kernels of the canonical projections on components of the multipullback 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.
Keywords
Cite
@article{arxiv.1008.0673,
title = {Quantum projective space from Toeplitz cubes},
author = {Piotr M. Hajac and Atabey Kaygun and Bartosz Zielinski},
journal= {arXiv preprint arXiv:1008.0673},
year = {2010}
}
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16 pages