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Quantum Isometries and Noncommutative Spheres

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Abstract

We introduce and study two new examples of noncommutative spheres: the half-liberated sphere, and the free sphere. Together with the usual sphere, these two spheres have the property that the corresponding quantum isometry group is “easy”, in the representation theory sense. We present as well some general comments on the axiomatization problem, and on the “untwisted” and “non-easy” case.

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Authors and Affiliations

  1. Department of Mathematics, Cergy-Pontoise University, 95000, Cergy-Pontoise, France

    Teodor Banica

  2. Theoretical Statistics and Mathematics Unit, 203 Barrackpore Trunk Road, Kolkata, 700 108, India

    Debashish Goswami

Authors
  1. Teodor Banica
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  2. Debashish Goswami
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Correspondence to Teodor Banica.

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Communicated by A. Connes

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Banica, T., Goswami, D. Quantum Isometries and Noncommutative Spheres. Commun. Math. Phys. 298, 343–356 (2010). https://doi.org/10.1007/s00220-010-1060-5

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  • DOI: https://doi.org/10.1007/s00220-010-1060-5

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