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Higher $\ell^2$-Betti numbers of universal quantum groups

  • Julien Bichon,
    Laboratoire de Mathématiques Blaise Pascal, Université Clermont Auvergne, Campus universitaire des Cézeaux, 3 place Vasarely, 63178 Aubière cedex, France
  • David Kyed,
    Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
  • Sven Raum,
    EPFL SB SMA, Station 8, CH-1015 Lausanne, Switzerland
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Abstract

We calculate all $\ell^2$-Betti numbers of the universal discrete Kac quantum groups $\hat{\mathrm U}^+_n$ as well as their half-liberated counterparts $\hat{\mathrm U}^*_n$.
Keywords: $\ell^2$-Betti number, free unitary quantum group, half-liberated unitary quantum group, free product formula, extension $\ell^2$-Betti number, free unitary quantum group, half-liberated unitary quantum group, free product formula, extension
MSC Classifications: 16T05, 46L65, 20G42 show english descriptions Hopf algebras and their applications [See also 16S40, 57T05]
Quantizations, deformations
Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
16T05 - Hopf algebras and their applications [See also 16S40, 57T05]
46L65 - Quantizations, deformations
20G42 - Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
 

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