Quantum subgroups of $SL_q(2)$ at roots of unity of arbitrary order

TL;DR

This paper completes the classification of quantum subgroups of the quantum group $SL_q(2)$ at roots of unity, identifying all Hopf algebra quotients of the quantum function algebra for arbitrary order roots of unity.

Contribution

It provides a comprehensive classification of quantum subgroups of $SL_q(2)$ at roots of unity of any order, extending previous results to all cases.

Findings

Complete classification of quantum subgroups at arbitrary roots of unity

Identification of all Hopf algebra quotients of $\

Extension of classification to all roots of unity

Abstract

We complete the classification of quantum subgroups of $SL_q(2)$ with $q$ a root of unity of arbitrary order, that is, Hopf algebra quotients of the quantum function algebras $\mathcal{O}_{q} (SL_2(\mathbb{C}))$.