Ergodic Coactions with Large Multiplicity and Monoidal Equivalence of Quantum Groups

  • Julien BichonEmail author
  • An De Rijdt
  • Stefaan Vaes


We construct new examples of ergodic coactions of compact quantum groups, in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter. These examples are obtained using a bijective correspondence between certain ergodic coactions on C*-algebras and unitary fiber functors on the representation category of a compact quantum group. We classify these unitary fiber functors on the universal orthogonal and unitary quantum groups. The associated C*-algebras and von Neumann algebras can be defined by generators and relations, but are not yet well understood.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques AppliquéesUniversité de Pau et des Pays de l'Adour, IPRA, Avenue de l'UniversitéPauFrance
  2. 2.Department of MathematicsK.U.LeuvenLeuvenBelgium
  3. 3.Institut de Mathématiques de JussieuAlgèbres d'OpérateursParisFrance

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