Separated monic correspondence of cotorsion pairs and semi-Gorenstein-projective modules

2022/10/31 by Luo, Xiu-Hua, Zhu, Shijie · 1 citation
#16B50 #16E65 #16G10 #16G50 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2210.17231

Abstract

Given a finite dimensional algebra A over a field k, and a finite acyclic quiver Q, let Λ= A⊗_k kQ/I, where kQ is the path algebra of Q over k and I is a monomial ideal. We show that (\mathcal X,\mathcal Y) is a (complete) hereditary cotorsion pair in A-mod if and only if (\rm smon(Q,I,\mathcal X), \rm rep(Q,I,\mathcal Y)) is a (complete) hereditary cotorsion pair in Λ-mod. We also show that A is left weakly Gorenstein if and only if so is Λ. Provided that kQ/I is non-semisimple, the category ^⊥Λ of semi-Gorenstein-projective Λ-modules coincides with the category of separated monic representations \rm smon(Q,I,^⊥A) if and only if A is left weakly Gorenstein.

Cited by

• Weakly Gorensteinness of tensor algebras and Morita algebras

Related

• Monic representations and Gorenstein-projective modules
• Monic monomial representations I Gorenstein-projective modules
• Monic modules and semi-Gorenstein-projective modules
• Chains of model structures arising from modules of finite Gorenstein dimension
• Categories of quiver representations and relative cotorsion pairs