Czechoslovak Mathematical Journal, Vol. 69, No. 4, pp. 925-943, 2019


The duality of Auslander-Reiten quiver of path algebras

Bo Hou, Shilin Yang

Received November 28, 2017.   Published online February 18, 2019.

Abstract:  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 $(\Gamma_Q, G)$.
Keywords:  Auslander-Reiten quiver; generalized McKay quiver; duality
Classification MSC:  16G10, 16G20, 16G70


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Affiliations:   Bo Hou, School of Mathematics and Statistics, Henan University, Ming Lun Street, Kaifeng, Henan, China, e-mail: bohou1981@163.com; Shilin Yang (corresponding author), College of Applied Sciences, Beijing University of Technology, 100 Ping Le Yuan, Chaoyang District, Beijing 100124, China, e-mail: slyang@bjut.edu.cn


 
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