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Keywords:
Auslander-Reiten quiver; generalized McKay quiver; duality
Auslander-Reiten quiver; generalized McKay quiver; duality
Summary:
Let $Q$ be a finite union of Dynkin quivers, $G\subseteq {\rm Aut}(\Bbbk {Q})$ a finite abelian group, $\widehat {Q}$ the generalized McKay quiver of $(Q, G)$ and $\Gamma _{Q}$ the Auslander-Reiten quiver of $\Bbbk Q$. Then $G$ acts functorially on the quiver $\Gamma _{Q}$. We show that the Auslander-Reiten quiver of $\Bbbk \widehat {Q}$ coincides with the generalized McKay quiver of $(\Gamma _{Q}, G)$.
References:
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