态射范畴的极大rigid对象  

On maximal rigid objects of morphism category

作　　者：李伟宇 LI Wei-Yu(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2021年第5期27-30,共4页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11971326)。

摘　　要：对任意数域k上的有限维代数Λ,记M为Λ的有限生成投射模态射范畴.本文利用Λ的支撑τ-倾斜模给出了M的极大rigid对象的分类.特别地,M的极大rigid对象与Λ的支撑τ-倾斜模之间存在一一对应关系.作为结果,M中的任意rigid对象都可以扩充为极大rigid对象,且任意的基本极大rigid对象的不可分解直和项个数恰好为2|Λ|.For a finite-dimensional algebra Λ over a field k,let M be the morphism category of finitely generated projective Λ-modules.We classify the maximal rigid objects of M by supportτ-tilting Λ-modules.In particular,there is a bijection between the set of maximal rigid objects of M and the set of support τ-tilting Λ-modules.As a result,every rigid object of M can be expanded into a maximal rigid object and each basic maximal rigid object of M has precisely 2|Λ| indecomposable direct summands.

关 键 词：态射范畴 极大rigid对象 支撑τ-倾斜模 

分 类 号：O154.2[理学—数学]