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Quantum Teardrops

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Abstract

Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops is described in detail. In particular the presentation of the coordinate algebra of the quantum teardrop in terms of generators and relations and classification of irreducible *-representations are derived. The algebras are then analysed from the point of view of Hopf-Galois theory or the theory of quantum principal bundles. Fredholm modules and associated traces are constructed. C*-algebras of continuous functions on quantum weighted projective lines are described and their K-groups computed.

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Authors and Affiliations

  1. Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK

    Tomasz Brzeziński & Simon A. Fairfax

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  1. Tomasz Brzeziński
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  2. Simon A. Fairfax
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Correspondence to Tomasz Brzeziński.

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Communicated by A. Connes

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Brzeziński, T., Fairfax, S.A. Quantum Teardrops. Commun. Math. Phys. 316, 151–170 (2012). https://doi.org/10.1007/s00220-012-1580-2

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  • DOI: https://doi.org/10.1007/s00220-012-1580-2

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