Gluing compact matrix quantum groups

TL;DR

This paper investigates the construction and characterization of glued tensor and free products of compact matrix quantum groups, introducing new concepts like global colourization and extending existing procedures.

Contribution

It provides a detailed analysis of glued quantum groups via their representation categories and algebraic relations, generalizing colourization concepts to all compact matrix quantum groups.

Findings

Characterization of glued tensor and free products.

Extension of colourization concepts to arbitrary compact matrix quantum groups.

Analysis of gluing and ungluing procedures.

Abstract

We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In addition, we generalize the concepts of global colourization and alternating colourings from easy quantum groups to arbitrary compact matrix quantum groups. Those concepts are closely related to tensor and free complexification procedures. Finally, we also study a more general procedure of gluing and ungluing.