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2021 Strongly Gorenstein-projective Quiver Representations
Tengxia Ju, Xiu-Hua Luo
Taiwanese J. Math. Advance Publication 1-13 (2021). DOI: 10.11650/tjm/201103

Abstract

Given a field $k$, a finite-dimensional $k$-algebra $A$, and a finite acyclic quiver $Q$, let $AQ$ be the path algebra of $Q$ over $A$. Then the category of representations of $Q$ over $A$ is equivalent to the category of $AQ$-modules. The main result of this paper explicitly describes the strongly Gorenstein-projective $AQ$-modules via the separated monic representations with a local strongly Gorenstein-property. As an application, a necessary and sufficient condition is given on when each Gorenstein-projective $AQ$-module is strongly Gorenstein-projective. As a direct result, for an integer $t \geq 2$, let $A = k[x]/\langle x^t \rangle$, each Gorenstein-projective $AQ$-module is strongly Gorenstein-projective if and only if $A = k[x]/\langle x^2 \rangle$.

Citation

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Tengxia Ju. Xiu-Hua Luo. "Strongly Gorenstein-projective Quiver Representations." Taiwanese J. Math. Advance Publication 1 - 13, 2021. https://doi.org/10.11650/tjm/201103

Information

Published: 2021
First available in Project Euclid: 30 November 2020

Digital Object Identifier: 10.11650/tjm/201103

Subjects:
Primary: 16E65, 16G10

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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