On the representation type of subcategories of derived categories
On the representation type of subcategories of derived categories
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论派生类别子类别的表示类型
DOI：
10.1142/s0219498820500322
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发表时间：
2019
影响因子：
0.8
通讯作者：
Zhang Chao
中科院分区：
文献类型：
--
作者：
Zhang Chao
设[Formula：see text]为有限维[Formula：see text]-代数。本文主要研究有界导范畴[公式：见正文]的子范畴的表示类型。首先，我们定义了子范畴的表示类型和上同调长度、宽度、值域等同调不变量。在这个框架下，我们提供了一个特征的派生离散代数。此外，对于有限维代数[Formula：see text]，我们建立了[Formula：see text]的某些逆变有限子范畴[Formula：see text]的第一Brauer-Thrall型定理，即[Formula：see text]是有限型的当且仅当它的上同调值域是有限的。
Let [Formula: see text] be a finite-dimensional [Formula: see text]-algebra. In this paper, we mainly study the representation type of subcategories of the bounded derived category [Formula: see text]. First, we define the representation type and some homological invariants including cohomological length, width, range for subcategories. In this framework, we provide a characterization for derived discrete algebras. Moreover, for a finite-dimensional algebra [Formula: see text], we establish the first Brauer–Thrall type theorem of certain contravariantly finite subcategories [Formula: see text] of [Formula: see text], that is, [Formula: see text] is of finite type if and only if its cohomological range is finite.