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C*-algebras and Elliptic Theory II pp 145–147Cite as

On the Non-standard Podleś Spheres

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Abstract

It was shown in [1, 5] that the C*-completion of Podleś’ generic quantum spheres A qρ [4] is independent of the parameter ρ. In the present note we provide a proof that this is not true for the A qρ themselves which remained a conjecture in [1]. As a byproduct we obtain that Aut(A qρ) = ℂx

This work was supported by the EU Marie Curie postdoctoral fellowship EIF 515144. It is a pleasure to thank the authors of [1] for pointing out to me this problem and for all the other discussions we had.

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References

  1. P.M. Hajac, R. Matthes, W. Szymański: Quantum Real Projective Space, Disc and Sphere. Algebr. Represent. Theory 6 No. 2 (2003), 169–192

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  5. A. Sheu: Quantization of the Poisson SU(2) and its Poisson Homogeneous Space — The 2-Sphere. Comm. Math. Phys. 155 (1991), 217–232

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Author information

Authors and Affiliations

  1. Mathematics Department, University of Glasgow University Gardens, Glasgow, G12 8QW, UK

    Ulrich Krähmer

Authors
  1. Ulrich Krähmer
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Editors and Affiliations

  1. Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, OH, 43210, USA

    Dan Burghelea

  2. Department of Mathematics, Massachusetts Institute of Technology, Room 2-174 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Richard Melrose

  3. Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119992, Moscow, Russia

    Alexander S. Mishchenko  & Evgenij V. Troitsky  & 

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Krähmer, U. (2008). On the Non-standard Podleś Spheres. In: Burghelea, D., Melrose, R., Mishchenko, A.S., Troitsky, E.V. (eds) C*-algebras and Elliptic Theory II. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8604-7_7

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