Calabi-Yau properties of Postnikov diagrams
Calabi-Yau properties of Postnikov diagrams
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Postnikov 图的 Calabi-Yau 性质
DOI：
10.1017/fms.2022.52
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Pressland M
中科院分区：
文献类型：
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作者：
Pressland M
我们证明了圆盘中连通的Postnikov图的二聚体代数在作者早期工作[43]的意义上是双模内部-Calabi-Yau。因此，我们得到了与图相关的聚类代数的一个加性分类，该分类（在对冻结变量进行逆变换后）与格拉斯曼正态变异的齐次坐标环同构（由Galashin和Lam[18]的最新结果得到）。我们证明了我们的分类可以被实现为Jensen-King-Su的Grassmannian聚类范畴[28]的一个完全扩展闭子范畴，以一种与它们在秩模和pl<s:1> cker坐标之间的双射相容的方式。
We show that the dimer algebra of a connected Postnikov diagram in the disc is bimodule internally -Calabi–Yau in the sense of the author’s earlier work [43]. As a consequence, we obtain an additive categorification of the cluster algebra associated to the diagram, which (after inverting frozen variables) is isomorphic to the homogeneous coordinate ring of a positroid variety in the Grassmannian by a recent result of Galashin and Lam [18]. We show that our categorification can be realised as a full extension closed subcategory of Jensen–King–Su’s Grassmannian cluster category [28], in a way compatible with their bijection between rank modules and Plücker coordinates.