Coideal subalgebras of quantum $SL_2$ at roots of unity

TL;DR

This paper classifies right coideal subalgebras of certain quantum groups at roots of unity, providing explicit generators and relations, advancing understanding of their algebraic structure.

Contribution

It provides a complete classification of right coideal subalgebras of quantum $SL_2$ at roots of unity, including explicit descriptions by generators and relations.

Findings

Classified right coideal subalgebras of $U_q(rak{sl}_2)$ and $ ext{O}_q(SL_2)$ at roots of unity.

Described all coideal subalgebras explicitly by generators and relations.

Enhanced understanding of the structure of quantum groups at roots of unity.

Abstract

We classify right coideal subalgebras of the finite-dimensional quotient of the quantized enveloping algebra $U_q(\mathfrak{sl}_2)$ and that of the quantized coordinate algebra $\mathcal{O}_q(SL_2)$ at a root of unity $q$ of odd order. All those coideal subalgebras are described by generators and relations.