Quantum projective space from Toeplitz cubes

2010/08/03 by Piotr M. Hajac, Hajac, Piotr M., Atabey Kaygun +3 · 3 citations
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1008.0673

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.

Cited by

• Milnor meets Hopf and Toeplitz at the K-theory of quantum projective planes
• Rank-two Milnor idempotents for the multipullback quantum complex projective plane
• Reductions of piecewise-trivial principal comodule algebras

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