Complete Cohomology for Extriangulated Categories  

作　　者：Jiangsheng Hu Dongdong Zhang Tiwei Zhao Panyue Zhou 

机构地区：[1]School of Mathematics and Physics,Jiangsu University of Technology Changzhou,Jiangsu 213001,China [2]Department of Mathematics,Zhejiang Normal University Jinhua,Zhejiang 321004,China [3]School of Mathematical Sciences,Qufu Normal University Qufu,Shandong 273165,China [4]College of Mathematics,Hunan Institute of Science and Technology Yueyang,Hunan 414006,China

出　　处：《Algebra Colloquium》2021年第4期701-720,共20页代数集刊（英文版）

基　　金：supported by the NSF of China(11671069,11771212);Qing Lan Project of Jiangsu Province and Natural Science Foundation of Jiangsu Province(BK20211358);supported by the NSF of China(11971225,11901341);Shandong Provincial Natural Science Foundation(ZR2019QA015);supported by the National Natural Science Foundation of China(11901190,11671221);the Hunan Provincial Natural Science Foundation of China(2018JJ3205);the Scientific Research Fund of Hunan Provincial Education Department(19B239).

摘　　要：Let(C,E,s)be an extriangulated category with a proper classξof E-triangles.We study complete cohomology of objects in(C,E,s)by applyingξ-projective resolutions andξ-injective coresolutions constructed in(C,E,s).Vanishing of complete cohomology detects objects with finiteξ-projective dimension and finiteξ-injective dimension.As a consequence,we obtain some criteria for the validity of the Wakamatsu tilting conjecture and give a necessary and sufficient condition for a virtually Gorenstein algebra to be Gorenstein.Moreover,we give a general technique for computing complete cohomology of objects with finiteξ-Gprojective dimension.As an application,the relations betweenξ-projective dimension andξ-Gprojective dimension for objects in(C,E,s)are given.

关 键 词：complete cohomology extriangulated category proper class Gorenstein projective dimension 

分 类 号：O15[理学—数学]