On support τ-tilting graphs of gentle algebras
On support τ-tilting graphs of gentle algebras
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DOI：
10.1016/j.jalgebra.2023.03.013
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发表时间：
2021-08
影响因子：
0.9
通讯作者：
Changjian Fu;Shengfei Geng;Ping Liu;Yu Zhou
中科院分区：
文献类型：
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作者：
Changjian Fu;Shengfei Geng;Ping Liu;Yu Zhou
LetAbe 是代数闭域上的有限维温和代数。我们研究了 A 的支持τ-倾斜图的组合特性。特别是，证明了A的支撑τ-倾斜图是连通的，并且具有所谓的面可达性。这个性质是 Fomin 和 Zelevinsky 针对簇代数交换图提出的猜想，最近被曹和李证实。
LetAbe a finite-dimensional gentle algebra over an algebraically closed field. We investigate the combinatorial properties of supportτ-tilting graph ofA. In particular, it is proved that the supportτ-tilting graph ofAis connected and has the so-called reachable-in-face property. This property was conjectured by Fomin and Zelevinsky for exchange graphs of cluster algebras which was recently confirmed by Cao and Li.