On Support τ-tilting Modules over Endomorphism Algebras of Rigid Ob jects  

作　　者：Wen CHANG Jie ZHANG Bin ZHU 

机构地区：[1]Department of Mathematical Sciences, Tsinghua University [2]School of Mathematics and Statistics, Beijing institute of technology

出　　处：《Acta Mathematica Sinica,English Series》2015年第9期1508-1516,共9页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11131001);supported by BIT Basic Scientific Research Grant(Grant No.3170012211408)

摘　　要：We consider a Krull-Schmidt, Hom-finite, 2-Calabi Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic T-rigid pairs in the module category of the endomorphism algebra Endc（T）op. As a consequence, basic maximal objects in prT are one-to-one correspondence to basic support τ-tilting modules over Endc（T）op. This is a generalization of correspondences established by Adachi-Iyama-Reiten.We consider a Krull-Schmidt, Hom-finite, 2-Calabi Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic T-rigid pairs in the module category of the endomorphism algebra Endc（T）op. As a consequence, basic maximal objects in prT are one-to-one correspondence to basic support τ-tilting modules over Endc（T）op. This is a generalization of correspondences established by Adachi-Iyama-Reiten.

关 键 词：Rigid object maximal rigid object τ-rigid object finite presented category 

分 类 号：O153[理学—数学]