2022/02/26 by Haiyu Liu, Liu, Haiyu, Rongmin Zhu +1
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2202.13148
Let A, B be two rings and T=(\beginsmallmatrix A & M 0 & B \endsmallmatrix) with M an A-B-bimodule. We first construct a semi-complete duality pair DT of T-modules using duality pairs in A-Mod and B-Mod respectively. Then we characterize when a left T-module is Gorenstein DT-projective, Gorenstein DT-injective or Gorenstein DT-flat. These three class of T-modules will induce model structures on T-Mod. Finally we show that the homotopy category of each of model structures above admits a recollement relative to corresponding stable categories. Our results give new characterizations to earlier results in this direction.