论文标题
在某些单态类别的稳定的Auslander-Reiten组件上
On the stable Auslander-Reiten components of certain monomorphism categories
论文作者
论文摘要
令$λ$为artin代数，让$ \ rm {gprj} \ mbox { - }λ$表示所有有限生成的Gorenstein Projective $λ$ -Modules的类。在本文中，我们研究了单态类别的某个子类别$ \ MATHCAL {S}（{\ rm gprj} \ mbox { - }λ）$的组成部分的组成部分。我们描述了此类组件的形状。结果表明，某些组件链接到稳定类别$ \ usepline {\ rm {gprj}} \ mbox { - }λ$的稳定类别上的自动等量的轨道。特别是，对于有限的组件，我们表明，在某些温和条件下，它们的红衣愿望可分配$ 3 $。我们看到，这种三个周期性现象在本文中多次重新占领。
Let $Λ$ be an Artin algebra and let $\rm{Gprj}\mbox{-}Λ$ denote the class of all finitely generated Gorenstein projective $Λ$-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a certain subcategory of the monomorphism category $\mathcal{S}({\rm Gprj}\mbox{-}Λ)$ containing boundary vertices. We describe the shape of such components. It is shown that certain components are linked to the orbits of an auto-equivalence on the stable category $\underline{\rm{Gprj}}\mbox{-}Λ$. In particular, for the finite components, we show that under certain mild conditions their cardinalities are divisible by $3$. We see that this three-periodicity phenomenon reoccurs several times in the paper.
