Cotorsion pairs in the cluster category of a marked surface
Cotorsion pairs in the cluster category of a marked surface
复制标题
标记表面的簇类别中的扭曲对
DOI：
10.1016/j.jalgebra.2013.06.014
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发表时间：
2012-05
影响因子：
0.9
通讯作者：
Zhu, Bin
中科院分区：
文献类型：
--
作者：
Zhang, Jie;Zhou, Yu;Zhu, Bin
We study extension spaces, cotorsion pairs and their mutations in the cluster category of a marked surface without punctures. Under the one-to-one correspondence between the curves, valued closed curves in the marked surface and the indecomposable objects in the associated cluster category, we prove that the dimension of extension space of two indecomposable objects in the cluster categories equals to the intersection number of the corresponding curves. By using this result, we prove that there are no non-trivialt-structures in the cluster categories when the surface is connected. Based on this result, we give a classification of cotorsion pairs in these categories. Moreover we define the notion of paintings of a marked surface without punctures and their rotations. They are a geometric model of cotorsion pairs and of their mutations respectively.
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DOI：
10.1070/im1989v033n01abeh000813
发表时间：
1989-02
期刊：
Mathematics of The Ussr-izvestiya
影响因子：
--
作者：
A. Gorodentsev
通讯作者：
A. Gorodentsev
影响因子：
1.7
作者：
B. Keller;D. Yang
通讯作者：
B. Keller;D. Yang
影响因子：
168.9
作者：
Nath, I;Reddy, KS;Valiathan, MS
通讯作者：
Valiathan, MS
影响因子：
0.6
作者：
H. Nakaoka
通讯作者：
H. Nakaoka
影响因子：
1.7
作者：
B. Keller;I. Reiten
通讯作者：
B. Keller;I. Reiten