Wide Subcategories are Semistable
Wide Subcategories are Semistable
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DOI：
10.4171/dm/612
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发表时间：
2017-05
影响因子：
0.9
通讯作者：
Toshiya Yurikusa
中科院分区：
文献类型：
--
作者：
Toshiya Yurikusa
对于任意有限维代数$\Lambda$，证明了满足一定有限条件的$\mathsf{mod} \Lambda$的任何宽子范畴对于某些稳定条件$\theta$是$\theta$ -半稳定的。更一般地说，我们表明与$\Lambda$的两期预印复合物相关的$\mathsf{mod} \Lambda$的广泛子类别是半稳定的。这为有限维代数的ingalls - thomas型双射提供了一个补充。
For an arbitrary finite dimensional algebra $\Lambda$, we prove that any wide subcategory of $\mathsf{mod} \Lambda$ satisfying a certain finiteness condition is $\theta$-semistable for some stability condition $\theta$. More generally, we show that wide subcategories of $\mathsf{mod} \Lambda$ associated with two-term presilting complexes of $\Lambda$ are semistable. This provides a complement for Ingalls-Thomas-type bijections for finite dimensional algebras.