当前位置:
X-MOL 学术
›
J. Algebra Appl.
›
论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Relative n-rigid objects in (n + 2)-angulated categories
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2020-07-15 , DOI: 10.1142/s0219498821501577 Zongyang Xie 1 , Zhongkui Liu 1 , Zhenxing Di 1
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2020-07-15 , DOI: 10.1142/s0219498821501577 Zongyang Xie 1 , Zhongkui Liu 1 , Zhenxing Di 1
Affiliation
Let k be an algebraically closed field, n ≥ 1 an integer, 𝒯 a k -linear Hom-finite ( n + 2 ) -angulated category with n -suspension functor Σ n , a Serre functor S , and split idempotents. Let T be a basic n -rigid object and Γ the endomorphism algebra of T . We introduce the notion of relative n -rigid objects, i.e. Σ n T -rigid objects of 𝒯 . Then we show that the basic maximal Σ n T -rigid objects in 𝒯 are in bijection with basic maximal τ n -rigid pairs of Γ -modules when every indecomposable object in 𝒯 is n -rigid. As an application, we recover a result in Jacobsen–Jø rgensen [Maximal τ d -rigid pairs, J. Algebra 546 (2020) 119–134].
中文翻译:
(n + 2) 角度类别中的相对 n 刚体对象
让ķ 是代数闭域,n ≥ 1 一个整数,𝒯 一种ķ -线性Hom-有限( n + 2 ) -有角度的类别n -悬浮函子Σ n , 一个 Serre 函子小号 ,并分裂幂等。让吨 做一个基本的n - 刚性物体和Γ 的自同态代数吨 . 我们引入相对的概念n - 刚性物体,即Σ n 吨 - 刚性物体𝒯 . 然后我们证明了基本最大值Σ n 吨 - 刚性物体𝒯 与基本最大值双射τ n -刚性对Γ -modules 当每个不可分解的对象𝒯 是n -死板的。作为应用程序,我们在 Jacobsen-J 中恢复结果Ø rgensen [最大τ d -刚性对,J.代数 546 (2020) 119–134]。
更新日期:2020-07-15
中文翻译:
(n + 2) 角度类别中的相对 n 刚体对象
让