The duality of Auslander-Reiten quiver of path algebras

Bo Hou; Shilin Yang

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 4, page 925-943
  • ISSN: 0011-4642

Abstract

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Let Q be a finite union of Dynkin quivers, G ⊆ Aut ( 𝕜 Q ) a finite abelian group, Q ^ the generalized McKay quiver of ( Q , G ) and Γ Q the Auslander-Reiten quiver of 𝕜 Q . Then G acts functorially on the quiver Γ Q . We show that the Auslander-Reiten quiver of 𝕜 Q ^ coincides with the generalized McKay quiver of ( Γ Q , G ) .

How to cite

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Hou, Bo, and Yang, Shilin. "The duality of Auslander-Reiten quiver of path algebras." Czechoslovak Mathematical Journal 69.4 (2019): 925-943. <http://eudml.org/doc/294277>.

@article{Hou2019,
abstract = {Let $Q$ be a finite union of Dynkin quivers, $G\subseteq \{\rm Aut\}(\mathbb \{k\}\{Q\})$ a finite abelian group, $\widehat\{Q\}$ the generalized McKay quiver of $(Q, G)$ and $\Gamma _\{Q\}$ the Auslander-Reiten quiver of $\mathbb \{k\}Q$. Then $G$ acts functorially on the quiver $\Gamma _\{Q\}$. We show that the Auslander-Reiten quiver of $\mathbb \{k\}\widehat\{Q\}$ coincides with the generalized McKay quiver of $(\Gamma _\{Q\}, G)$.},
author = {Hou, Bo, Yang, Shilin},
journal = {Czechoslovak Mathematical Journal},
keywords = {Auslander-Reiten quiver; generalized McKay quiver; duality},
language = {eng},
number = {4},
pages = {925-943},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The duality of Auslander-Reiten quiver of path algebras},
url = {http://eudml.org/doc/294277},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Hou, Bo
AU - Yang, Shilin
TI - The duality of Auslander-Reiten quiver of path algebras
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 925
EP - 943
AB - Let $Q$ be a finite union of Dynkin quivers, $G\subseteq {\rm Aut}(\mathbb {k}{Q})$ a finite abelian group, $\widehat{Q}$ the generalized McKay quiver of $(Q, G)$ and $\Gamma _{Q}$ the Auslander-Reiten quiver of $\mathbb {k}Q$. Then $G$ acts functorially on the quiver $\Gamma _{Q}$. We show that the Auslander-Reiten quiver of $\mathbb {k}\widehat{Q}$ coincides with the generalized McKay quiver of $(\Gamma _{Q}, G)$.
LA - eng
KW - Auslander-Reiten quiver; generalized McKay quiver; duality
UR - http://eudml.org/doc/294277
ER -

References

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