Homological systems in module categories over pre-ordered sets
Homological systems in module categories over pre-ordered sets
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模块类别中预排序集的同源系统
DOI：
10.1093/qmath/han003
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Changchang Xi
中科院分区：
文献类型：
--
作者：
O. Mendoza;C. Sáenz;Changchang Xi
在预序集上的模范畴中引入所谓的同调系统，推广了线性序集上的分层系统的概念，并研究了相应的由系统过滤的模和由系统分层的代数。特别地，我们恢复了准标准分层代数的倾斜理论，得到了用标准模和单模计算准标准分层代数的Cartan行列式的一般公式。此外，还讨论了给定代数的有限维，以及与同调系相关的模的满子范畴的相对同调维。作为应用，我们得到了准标准分层代数的有限维的一个新的界。
We introduce the so-called homological systems in a module category over a pre-ordered set, which generalize the notion of a stratifying system over a linearly ordered set, and study both the corresponding modules filtrated by the systems and algebras stratified by the systems. In particular, we recover the tilting theory for pre-standardly stratified algebras, and get a general formula for computing the Cartan determinants of pre-standardly stratified algebras in terms of standard modules and simple modules. Also, the finitistic dimension of a given algebra, and the relative homological dimensions of full subcategories of the modules related to a homological system, are discussed. As an application, we get a new bound for the finitistic dimension of a pre-standardly stratified algebra.