Modelling questions for transitive quantum groups

TL;DR

This survey explores transitive quantum groups and their flat matrix models, summarizing known results, recent improvements, and open problems in the field of quantum algebra and Hopf algebras.

Contribution

It provides a comprehensive review with new results and generalizations on transitive quantum groups and their matrix models, advancing understanding in quantum algebra.

Findings

Reviewed known results on transitive quantum groups

Presented new technical generalizations and improvements

Discussed open problems and future directions

Abstract

This is a survey on the transitive quantum groups $G\subset S_N^+$, and on the flat matrix models $\pi:C(G)\to M_N(C(X))$ for the corresponding Hopf algebras. We review the known results on the subject, with a number of improvements, technical generalizations, and some new results as well, and we discuss the open problems.