发表机构
Shanghai Jiao Tong University（上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
利用完全乘法公式研究簇特征的syzygy与suspension，在2-Calabi-Yau范畴中建立逆自同构与传递原理，推广扭曲恒等式并恢复相关公式。
AI 中文摘要
我们利用完全乘法公式研究簇特征的syzygy与suspension。在稳定2-Calabi--Yau Frobenius范畴中，syzygy与cosyzygy诱导局部化特征代数的互逆自同构；在Hom-有限2-Calabi--Yau三角范畴中，同一唯一性原理在suspension下传递所有簇特征。后者给出我们的Auslander--Reiten $F$-多项式恒等式。无需突变可达性。我们将positroid扭曲恒等式推广到所有对象，恢复Grassmannian与单幂胞公式，在边界局域化前识别配分函数代数，并在相关热带坐标映射为同胚时导出热带协变性。
英文摘要
We use the full multiplication formula to study syzygy and suspension of cluster characters. In stably 2-Calabi--Yau Frobenius categories, syzygy and cosyzygy induce inverse automorphisms of localized character algebras; in Hom-finite 2-Calabi--Yau triangulated categories, the same uniqueness principle transports all cluster characters under suspension. The latter gives our Auslander--Reiten $F$-polynomial identity. No mutation reachability is required. We extend positroid twist identities to all objects, recover the Grassmannian and unipotent-cell formulas, identify partition-function algebras before boundary localization, and derive tropical covariance when the relevant tropical coordinate map is a homeomorphism.
Comments28 pages, comments are welcome
