Module algebras on truncated quantum planes over small quantum groups

Let $q$ be a $2n$-th primitive root of unity and ${\mathfrak{u}}_q({\mathfrak{s}\mathfrak{l}}_2)$ a small quantum group in the usual way. Under reasonable simplifying assumptions, we provided a complete classification of all ${\mathfrak{u}}_q({\mathfrak{s}\mathfrak{l}}_2)$-module algebras on the truncated quantum plane $A_{n,q}[x,y]$, which was generated by $x$, $y$ subject to the relations: $yx=qxy,x^n=y^n=0.$