Report on the finiteness of silting objects
Report on the finiteness of silting objects
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DOI：
10.1017/s0013091521000109
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发表时间：
2020-02
影响因子：
0.7
通讯作者：
T. Aihara;T. Honma;K. Miyamoto;Qi Wang
中科院分区：
文献类型：
--
作者：
T. Aihara;T. Honma;K. Miyamoto;Qi Wang
本文讨论了（二项）淤积物的有限性。首先，我们研究了新的三角分类没有淤积对象。其次，研究了两类$\tau$-倾斜有限代数，给出了它们的双项淤积对象的个数。最后，我们研究了$\tau$-倾斜有限性蕴涵表示有限性的条件，得到了几类$\tau$-倾斜有限代数是表示有限的代数.
Abstract We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without silting object. Second, we study two classes of $\tau$-tilting-finite algebras and give the numbers of their two-term silting objects. Finally, we explore when $\tau$-tilting-finiteness implies representation-finiteness and obtain several classes of algebras in which a $\tau$-tilting-finite algebra is representation-finite.