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Quantum Weighted Projective and Lens Spaces

Abstract

We generalize to quantum weighted projective spaces in any dimension previous results of us on K-theory and K-homology of quantum projective spaces ‘tout court’. For a class of such spaces, we explicitly construct families of Fredholm modules, both bounded and unbounded (that is, spectral triples), and prove that they are linearly independent in the K-homology of the corresponding C *-algebra. We also show that the quantum weighted projective spaces are base spaces of quantum principal circle bundles whose total spaces are quantum lens spaces. We construct finitely generated projective modules associated with the principal bundles and pair them with the Fredholm modules, thus proving their non-triviality.

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Correspondence to Francesco D’Andrea.

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Communicated by Y. Kawahigashi

Dedicated to Marc Rieffel on the occasion of his 75th birthday

This work was partially supported by the Italian Project “Prin 2010-11—Operator Algebras, Noncommutative Geometry and Applications”. F.D. was partially supported by UniNA and Compagnia di San Paolo under the Program STAR 2013.

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D’Andrea, F., Landi, G. Quantum Weighted Projective and Lens Spaces. Commun. Math. Phys. 340, 325–353 (2015). https://doi.org/10.1007/s00220-015-2450-5

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  • DOI: https://doi.org/10.1007/s00220-015-2450-5

Keywords

  • Irreducible Representation
  • Weight Vector
  • Projective Space
  • Dirac Operator
  • Weighted Shift