On the Non-standard Podleś Spheres

  • Ulrich Krähmer
Part of the Trends in Mathematics book series (TM)


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


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  1. [1]
    P.M. Hajac, R. Matthes, W. Szymański: Quantum Real Projective Space, Disc and Sphere. Algebr. Represent. Theory 6 No. 2 (2003), 169–192zbMATHCrossRefGoogle Scholar
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    A. Joseph: Quantum Groups and Their Primitive Ideals. Springer, 1995Google Scholar
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    A.U. Klimyk, K. Schmüdgen: Quantum Groups and Their Representations. Springer, 1997Google Scholar
  4. [4]
    P. Podleś: Quantum Spheres. Lett. Math. Phys. 14 (1987), 193–202CrossRefMathSciNetGoogle Scholar
  5. [5]
    A. Sheu: Quantization of the Poisson SU(2) and its Poisson Homogeneous Space — The 2-Sphere. Comm. Math. Phys. 155 (1991), 217–232CrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Ulrich Krähmer
    • 1
  1. 1.Mathematics DepartmentUniversity of Glasgow University GardensGlasgowUK

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