The intertwiner spaces of non-easy group-theoretical quantum groups

TL;DR

This paper characterizes the intertwiner spaces of non-easy group-theoretical quantum groups by generalizing partition categories and employing a fiber functor, expanding understanding beyond easy quantum groups.

Contribution

It introduces a new approach to determine intertwiner spaces for non-easy group-theoretical quantum groups using generalized partition categories and a modified fiber functor.

Findings

Intertwiner spaces are explicitly characterized for non-easy group-theoretical quantum groups.

A generalized partition category framework is developed for these quantum groups.

The method extends the understanding of quantum symmetries beyond easy quantum groups.

Abstract

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.