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The Geometry of Quantum Lens Spaces: Real Spectral Triples and Bundle Structure

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Abstract

We study almost real spectral triples on quantum lens spaces, as orbit spaces of free actions of cyclic groups on the spectral geometry on the quantum group S U q (2). These spectral triples are given by weakening some of the conditions of a real spectral triple. We classify the irreducible almost real spectral triples on quantum lens spaces and we study unitary equivalences of such quantum lens spaces. Applying a useful characterization of principal U(1)-fibrations in noncommutative geometry, we show that all such quantum lens spaces are principal U(1)-fibrations over quantum teardrops.

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Authors and Affiliations

  1. Institute of Physics, Jagiellonian University, ul. prof. Stanisława Łojasiewicza 11, 30-348, Kraków, Poland

    Andrzej Sitarz

  2. Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, Warszawa, 00-950, Poland

    Andrzej Sitarz

  3. Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstraße 3-5, D-37073, Göttingen, Deutschland

    Jan Jitse Venselaar

Authors
  1. Andrzej Sitarz
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  2. Jan Jitse Venselaar
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Correspondence to Jan Jitse Venselaar.

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Partially supported by NCN grant 2011/01/B/ST1/06474.

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Sitarz, A., Venselaar, J.J. The Geometry of Quantum Lens Spaces: Real Spectral Triples and Bundle Structure. Math Phys Anal Geom 18, 9 (2015). https://doi.org/10.1007/s11040-015-9179-4

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  • DOI: https://doi.org/10.1007/s11040-015-9179-4

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