In 2015, Raum and Weber gave a definition of group-theoretical quantum groups, a class of compact matrix quantum groups with a certain presentation as semi-direct product quantum groups, and studied the case of easy quantum groups. In this article we determine the intertwiner spaces of non-easy group-theoretical quantum groups. We generalise group-theoretical categories of partitions and use a fiber functor to map partitions to linear maps which is slightly different from the one for easy quantum groups.We show that this construction provides the intertwiner spaces of group-theoretical quantum groups in general.
Cite this article
Laura Maaßen, The intertwiner spaces of non-easy group-theoretical quantum groups. J. Noncommut. Geom. 14 (2020), no. 3, pp. 987–1017DOI 10.4171/JNCG/384