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Semidirect Products of C*-Quantum Groups: Multiplicative Unitaries Approach

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Abstract

C*-quantum groups with projection are the noncommutative analogues of semidirect products of groups. Radford’s Theorem about Hopf algebras with projection suggests that any C*-quantum group with projection decomposes uniquely into an ordinary C*-quantum group and a “braided” C*-quantum group. We establish this on the level of manageable multiplicative unitaries.

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Authors and Affiliations

  1. Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstraße 3–5, 37073, Göttingen, Germany

    Ralf Meyer

  2. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, K1S 5B6, Canada

    Sutanu Roy

  3. Instytut Matematyczny Polskiej Akademii Nauk, ul. Śniadeckich 8, 00-656, Warsaw, Poland

    Stanisław Lech Woronowicz

  4. Katedra Metod Matematycznych Fizyki, Wydział Fizyki, Uniwersytet Warszawski, ul. Pasteura 5, 02-093, Warsaw, Poland

    Stanisław Lech Woronowicz

Authors
  1. Ralf Meyer
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  2. Sutanu Roy
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  3. Stanisław Lech Woronowicz
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Correspondence to Sutanu Roy.

Additional information

Communicated by Y. Kawahigashi

Supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Research Training Group 1493. The second author was also supported by a Fields–Ontario postdoctoral fellowship. The third author was partially supported by the Alexander von Humboldt-Stiftung and the National Science Center (NCN), grant 2015/17/B/ST1/00085.

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Meyer, R., Roy, S. & Woronowicz, S.L. Semidirect Products of C*-Quantum Groups: Multiplicative Unitaries Approach. Commun. Math. Phys. 351, 249–282 (2017). https://doi.org/10.1007/s00220-016-2727-3

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  • DOI: https://doi.org/10.1007/s00220-016-2727-3

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