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  • Titel
    Generalized fixed point algebras for coactions of locally compact quantum groups
  • Verfasser
    Buss, Alcides
  • Enthalten in
    Münster Journal of Mathematics, H. Münster Journal of Mathematics, S. 295-341
  • Erschienen
    2013
  • Sprache
    Englisch
  • Dokumenttyp
    Aufsatz in einer Zeitschrift
  • URN
    urn:nbn:de:hbz:6-55309458340 
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Abstract
  • We extend the construction of generalized fixed point algebras to the setting of locally compact quantum groups – in the sense of Kustermans and Vaes – following the treatment of Marc Rieffel, Ruy Exel and Ralf Meyer in the group case. We mainly follow Meyer’s approach analyzing the constructions in the realm of equivariant Hilbert modules. We generalize the notion of continuous square-integrability, which is exactly what one needs in order to define generalized fixed point algebras. As in the group case, we prove that there is a correspondence between continuously square-integrable Hilbert modules over an equivariant C*-algebra B and Hilbert modules over the reduced crossed product of B by the underlying quantum group. The generalized fixed point algebra always appears as the algebra of compact operators of the associated Hilbert module over the reduced crossed product.
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