Quiver representations and Gorenstein-projective modules

• Main Author: Francesco Meazzini
• Format: Article
• Language: English
• Published: Sapienza Università Editrice 2021-01-01
• Series: Rendiconti di Matematica e delle Sue Applicazioni
• Subjects: quiver representations; gorenstein-projective modules; model categories.
• Online Access: https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2021(1)/1-33.pdf

Consider a finite acyclic quiver Q and a quasi-Frobenius ring R. We endow the category of quiver representations over R with a model structure, whose homotopy category is equivalent to the stable category of Gorenstein-projective modules over the path algebra RQ. As an application, we then characterize Gorenstein-projective RQ-modules in terms of the corresponding quiver R-representations; this generalizes a result obtained by Luo-Zhang to the case of not necessarily finitely generated RQ-modules, and partially recover results due to Enochs-Estrada-Garc´ıa Rozas, and to Eshraghi-Hafezi-Salarian. Our approach to the problem is completely different since the proofs mainly rely on model category theory.