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We consider the action of a semisimple Hopf algebra $H$ on an $m$-KoszulArtin-Schelter regular algebra $A$. Such an algebra $A$ is aderivation-quotient algebra for some twisted superpotential $\mathsf{w}$, andwe show that the homological determinant of the action of $H$ on $A$ can beeasily calculated using $\mathsf{w}$. Using this, we show that the smashproduct $A\,\#\,H$ is also a derivation-quotient algebra, and use this toexplicitly determine a quiver algebra $\Lambda$ to which $A\,\#\,H$ is Moritaequivalent, generalising a result of Bocklandt-Schedler-Wemyss. We also showhow $\Lambda$ can be used to determine whether the Auslander map is anisomorphism. We compute a number of examples, and show how several results forthe quantum Kleinian singularities studied by Chan-Kirkman-Walton-Zhang followusing our techniques.

Superpotentials and Quiver Algebras for Semisimple Hopf Actions