Homological Transfer between Additive Categories and Higher Differential Additive Categories  

作　　者：Xi TANG Zhao Yong HUANG 

机构地区：[1]School of Science,Guilin University of Aerospace Technology,Guilin 541004,P.R.China [2]Department of Mathematics,Nanjing University,Nanjing 210093,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第5期1325-1344,共20页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.12371038,11971225,12171207,12061026);NSF of Guangxi Province of China(Grant No.2020GXNSFAA159120)。

摘　　要：Given an additive category C and an integer n≥2.The higher differential additive category consists of objects X in C equipped with an endomorphism ϵ_(X)satisfying ϵ_(X)^(n).Let R be a,finite-dimensional basic algebra over an algebraically closed field and T the augmenting functor from the category of finitely generated left R-modules to that of finitely generated left R/(t^(n))-modules.It is proved that a finitely generated left R-module M isτ-rigid(respectively,(support)τ-tilting,almost completeτ-tilting)if and only if so is T(M)as a left R[t]/(t^(n))-module.Moreover,R isτm-selfinjective if and only if so is R[t]/(t^(n)).

关 键 词：Higher differential objects Wakamatsu tilting subcategories G_(ω)-projective modules sup-portτ-tilting modules τ_(m)-selfinjective algebras precluster tilting subcategories 

分 类 号：O154.1[理学—数学]