Strong global dimensions of triangulated categories with respect to silting objects
Strong global dimensions of triangulated categories with respect to silting objects
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关于淤积物体的三角类别的强大全局维度
DOI：
10.1080/00927872.2019.1617871
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发表时间：
2019
影响因子：
0.7
通讯作者：
Hongjin Liu
中科院分区：
文献类型：
--
作者：
Qinghua Chen;Hongjin Liu
设T是一个具有淤积对象T的三角范畴，定义关于T的强整体维是T中所有不可分解对象的长度的最大值，证明了它是一个遗传三角范畴当且仅当T是有限的.本文还给出了三角等价下的强整体维度的界。此外，根据淤积对象构造了一类聚类倾斜子范畴。
Abstract Let be an triangulated category with a silting object T. The strong global dimension of with respect to T is defined to be the maximum of the length of all indecomposable objects in denoted by T- It is proved that is a hereditary triangulated category if and only if T- is finite. This article also gives the bounds of strong global dimensions under triangle equivalences. Moreover, a class of cluster tilting subcategories is constructed by the silting objects.