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Non-Semi-Regular Quantum Groups Coming from Number Theory

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Abstract:

 In this paper, we study C*-algebraic quantum groups obtained through the bicrossed product construction. Examples using groups of adeles are given and they provide the first examples of locally compact quantum groups which are not semi-regular: the crossed product of the quantum group acting on itself by translations does not contain any compact operator. We describe all corepresentations of these quantum groups and the associated universal C*-algebras. On the way, we provide several remarks on C*-algebraic properties of quantum groups and their actions.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Pures, Université Blaise Pascal, Bâtiment de Mathématiques, 63177 Aubière Cedex, France. E-mail: Saad.Baaj@math.univ-bpclermont.fr, , , , , , FR

    Saad Baaj

  2. Institut de Mathématiques de Jussieu, Algèbres d'Opérateurs et Représentations, 175, rue du Chevaleret, 75013 Paris, France. E-mail: skandal@math.jussieu.fr; vaes@math.jussieu.fr, , , , , , FR

    Georges Skandalis & Stefaan Vaes

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  1. Saad Baaj
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  2. Georges Skandalis
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  3. Stefaan Vaes
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Received: 10 October 2002 / Accepted: 10 October 2002 Published online: 24 January 2003

Communicated by A. Connes

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Baaj, S., Skandalis, G. & Vaes, S. Non-Semi-Regular Quantum Groups Coming from Number Theory. Commun. Math. Phys. 235, 139–167 (2003). https://doi.org/10.1007/s00220-002-0780-6

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  • DOI: https://doi.org/10.1007/s00220-002-0780-6

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