Volume 42_1_(2021)_1-33

Quiver representations and Gorenstein-projective modules
Francesco Meazzini

Abstract. 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-García Rozas, and to Eshraghi-Hafezi-Salarian. Our approach to the problem is completely different since the proofs mainly rely on model category theory.

Rend. Mat. Appl. (7) 42 (2021) 1-33;  pdf