Module algebras on truncated quantum planes over small quantum groups

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Abstract

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

Keywords

truncated quantum plane / small quantum group / module algebra

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