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The duality of Auslander-Reiten quiver of path algebras
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 925-943
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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 $(\Gamma _{Q}, G)$.
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 $(\Gamma _{Q}, G)$.
DOI : 10.21136/CMJ.2019.0541-17
Classification : 16G10, 16G20, 16G70
Keywords: Auslander-Reiten quiver; generalized McKay quiver; duality 
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Hou, Bo; Yang, Shilin. The duality of Auslander-Reiten quiver of path algebras. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 925-943. doi: 10.21136/CMJ.2019.0541-17

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