Communications in Mathematical Physics

, Volume 331, Issue 2, pp 677–701 | Cite as

CCAP for Universal Discrete Quantum Groups

  • Kenny De Commer
  • Amaury Freslon
  • Makoto YamashitaEmail author


We show that the discrete duals of the free orthogonal quantum groups have the Haagerup property and the completely contractive approximation property. Analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite-dimensional C*-algebras. The proof relies on the monoidal equivalence between free orthogonal quantum groups and SU q (2) quantum groups, on the construction of a sufficient supply of bounded central functionals for SU q (2) quantum groups, and on the free product techniques of Ricard and Xu. Our results generalize previous work in the Kac setting due to Brannan on the Haagerup property, and due to the second author on the CCAP.


Quantum Group Free Product Cartan Subalgebra Compact Quantum Group Central Functional 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Kenny De Commer
    • 1
  • Amaury Freslon
    • 2
  • Makoto Yamashita
    • 3
    Email author
  1. 1.Département de mathématiques, UMR CNRS 8088Université de Cergy-PontoiseCergy-PontoiseFrance
  2. 2.Sorbonne Paris Cité, UMR 7586Université Paris DiderotParisFrance
  3. 3.Institut for Matematiske FagKøbenhavns UniversitetCopenhagenDenmark

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