Mathematische Annalen

, Volume 369, Issue 3–4, pp 957–975 | Cite as

On the \({\ell }^2\)-Betti numbers of universal quantum groups

  • David Kyed
  • Sven Raum


We show that the first \({\ell }^2\)-Betti number of the duals of the free unitary quantum groups is one, and that all \({\ell }^2\)-Betti numbers vanish for the duals of the quantum automorphism groups of full matrix algebras.


\({\ell }^2\)-Betti numbers Free unitary quantum groups Quantum automorphism groups 

Mathematics Subject Classification

16T05 46L52 



The authors thank Julien Bichon for pointing out the reference [10], which provides a reference for the result shown in the “Appendix”.


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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark
  2. 2.EPFL SB SMALausanneSwitzerland

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