Recollements associated to cotorsion pairs over upper triangular matrix rings

2019/11/06 by Zhu, Rongmin, Peng, Yeyang, Ding, Nanqing
#Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.02478

Abstract

Let A, B be two rings and T=(\beginsmallmatrix A & M 0 & B \endsmallmatrix) with M an A-B-bimodule. Given two complete hereditary cotorsion pairs (A_A,B_A) and (C_B,D_B) in A-Mod and B-Mod respectively. We define two cotorsion pairs (Φ(A_A,C_B), Rep(B_A,D_B)) and (Rep(A_A,C_B), Ψ(B_A,D_B)) in T-Mod and show that both of these cotorsion pairs are complete and hereditary. Given two cofibrantly generated model structures M_A and M_B on A-Mod and B-Mod respectively. Using the result above, we investigate when there exist a cofibrantly generated model structure M_T on T-Mod and a recollement of Ho(M_T) relative to Ho(M_A) and Ho(M_B). Finally, some applications are given in Gorenstein homological algebra.

Related

• Cotorsion pairs and model structures on Morita rings
• Gorenstein and duality pair over triangular matrix rings
• n-cotorsion pairs over formal triangular matrix rings
• Gorenstein projective modules and recollements over triangular matrix rings
• Chains of model structures arising from modules of finite Gorenstein dimension