Quantum subgroups of a simple quantum group at roots of 1

TL;DR

This paper classifies all Hopf algebra quotients of the quantized coordinate algebra of a simple complex algebraic group at roots of unity, providing a comprehensive understanding of quantum subgroups at roots of 1.

Contribution

It explicitly determines all Hopf algebra quotients of the quantized coordinate algebra for simple algebraic groups at roots of unity, extending the understanding of quantum subgroups.

Findings

Complete classification of Hopf algebra quotients at roots of unity

Identification of quantum subgroups corresponding to these quotients

Clarification of the structure of quantum groups at roots of 1

Abstract

Let G be a connected, simply connected, simple complex algebraic group and let e be a primitive l-th root of 1, with l odd and 3 does not divide l if G is of type G_{2}. We determine all Hopf algebra quotients of the quantized coordinate algebra of G at e.