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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
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 Σn, 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. ΣnT-rigid objects of 𝒯. Then we show that the basic maximal ΣnT-rigid objects in 𝒯 are in bijection with basic maximal τn-rigid pairs of Γ-modules when every indecomposable object in 𝒯 is n-rigid. As an application, we recover a result in Jacobsen–Jørgensen [Maximal τd-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

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Σn, 一个 Serre 函子小号,并分裂幂等。让做一个基本的n- 刚性物体和Γ的自同态代数. 我们引入相对的概念n- 刚性物体,即Σn- 刚性物体𝒯. 然后我们证明了基本最大值Σn- 刚性物体𝒯与基本最大值双射τn-刚性对Γ-modules 当每个不可分解的对象𝒯n-死板的。作为应用程序,我们在 Jacobsen-J 中恢复结果Ørgensen [最大τd-刚性对,J.代数 546(2020) 119–134]。
更新日期:2020-07-15
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