Quiver representations over a quasi-Frobenius ring and Gorenstein-projective modules
arXiv:1610.04137
Abstract
We consider a finite acyclic quiver and a quasi-Frobenius ring . We endow the category of quiver representations over with a model structure, whose homotopy category is equivalent to the stable category of Gorenstein-projective modules over the path algebra . As an application, we then characterize Gorenstein-projective -modules in terms of the corresponding quiver -representations; this generalizes a result obtained by Luo-Zhang to the case of not necessarily finitely generated -modules, and partially recover results due to Enochs-Estrada-García Rozas, and to Eshraghi-Hafezi-Salarian. Our approach to the problem is completely different since the proofs mainly rely on model category theory.
Post-print version; accepted for publication in Rendiconti di Matematica e delle sue Applicazioni