Quantum subgroups of simple twisted quantum groups at roots of one

TL;DR

This paper classifies all Hopf algebra quotients of twisted multiparameter quantum function algebras at roots of unity for simple complex algebraic groups, extending previous untwisted case results.

Contribution

It provides a complete classification of quantum subgroups for twisted quantum groups at roots of unity, generalizing earlier work on untwisted cases.

Findings

All Hopf algebra quotients of the twisted quantum function algebra are determined.

The classification extends known results from untwisted to twisted quantum groups.

Results apply to simple complex algebraic groups with specific root of unity conditions.

Abstract

Let $G$ be a connected, simply connected simple complex algebraic group and let $\epsilon$ be a primitive $\ell$th root of unity with $\ell$ odd and coprime with $3$ if $G$ is of type $G_{2}$. We determine all Hopf algebra quotients of the twisted multiparameter quantum function algebra $\mathcal{O}_{\epsilon}^{\varphi}(G)$ introduced by Costantini and Varagnolo. This extends the results of Andruskiewitsch and the first author, where the untwisted case is treated.