Wreath products of finite groups by quantum groups

  • Amaury Freslon

    Université Paris-Sud, Orsay, France
  • Adam Skalski

    Polish Academy of Sciences, Warsaw, Poland
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Abstract

We introduce a notion of partition wreath product of a finite group by a partition quantum group, a construction motivated on the one hand by classical wreath products and on the other hand by the free wreath product of J. Bichon.We identify the resulting quantum group in several cases, establish some of its properties and show that when the finite group in question is abelian, the partition wreath product is itself a partition quantum group. This allows us to compute its representation theory, using earlier results of the first named author.

Cite this article

Amaury Freslon, Adam Skalski, Wreath products of finite groups by quantum groups. J. Noncommut. Geom. 12 (2018), no. 1, pp. 29–68

DOI 10.4171/JNCG/270