The bounded derived categories of an algebra with radical squared zero
The bounded derived categories of an algebra with radical squared zero
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DOI：
10.1016/j.jalgebra.2017.04.006
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发表时间：
2016-10
期刊：
影响因子：
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通讯作者：
R. Bautista;Shiping Liu
中科院分区：
文献类型：
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作者：
R. Bautista;Shiping Liu
设Λ是一个根平方为零的域上的初等局部有界线性范畴.本文证明了可分次左Λ-模的有界导范畴D B（Mod B Λ）有一个Galois覆盖，它是可分次左Λ-模的几乎余表现的有界导范畴。限制到有限维左Λ-模的有界导出范畴D B（mod B Λ），我们将能够描述它的不可分解对象，得到它的Auslander-Reiten分支形状的完整描述，并对这些Λ进行分类，使得D B（mod B Λ）只有1/2个Auslander-Reiten分支.
Let Λ be an elementary locally bounded linear category over a field with radical squared zero. We shall show that the bounded derived category D b (Mod b Λ) of finitely supported left Λ-modules admits a Galois covering which is the bounded derived category of almost finitely co-presented representations of a gradable quiver. Restricting to the bounded derived category D b (mod b Λ) of finite dimensional left Λ-modules, we shall be able to describe its indecomposable objects, obtain a complete description of the shapes of its Auslander–Reiten components, and classify those Λ such that D b (mod b Λ) has only finitely many Auslander–Reiten components.