Journal of Noncommutative Geometry

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Volume 12, Issue 1, 2018, pp. 29–68
DOI: 10.4171/JNCG/270

Published online: 2018-03-23

Wreath products of finite groups by quantum groups

Amaury Freslon[1] and Adam Skalski[2]

(1) Université Paris-Sud, Orsay, France
(2) Polish Academy of Sciences, Warsaw, Poland

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.

Keywords: Quantum groups, wreath product, representation theory

Freslon Amaury, Skalski Adam: Wreath products of finite groups by quantum groups. J. Noncommut. Geom. 12 (2018), 29-68. doi: 10.4171/JNCG/270