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

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Abstract

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.

Keywords

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

Mathematics Subject Classification

16T05 46L52 

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Copyright information

© 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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