Coideal subalgebras of quantum $S{L}_2$ at roots of unity

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