AI 中文总结
本文在Hom-有限2-Calabi-Yau Frobenius扩张三角范畴中，证明带簇倾斜对象的Wang-Wei-Zhang簇特征乘法公式，推广一维及稳定情形结果，并用最小余合冲中间项表达Auslander-Reiten网格冻结项，在Higgs范畴计算冻结重数获得主系数网格关系。
AI 中文摘要
我们证明了 Wang-Wei-Zhang 簇特征在一个 Hom-有限 $2$-Calabi--Yau Frobenius 扩张三角范畴 $\mathcal C$ 上的乘法公式，该范畴带有一个簇倾斜对象，并假设其稳定范畴相对于诱导的簇倾斜对象具有可构造锥。此公式推广了 Wang-Wei-Zhang 在一维情形下对 $\mathcal C$ 所得的结果，以及 Keller-Plamondon-Qin 对（稳定）$2$-Calabi-Yau Frobenius 或三角范畴所得的结果。作为推论，我们用最小余合冲中间项的簇特征表达了 Auslander-Reiten 网格中的冻结项。对于具有主系数的无圈箭图，我们在 Higgs 范畴中计算了这些冻结重数，并获得了显式的主系数网格关系。
英文摘要
We prove a multiplication formula for the Wang-Wei-Zhang cluster character on a Hom-finite $2$-Calabi--Yau Frobenius extriangulated category $\mathcal C$ with a cluster-tilting object under the assumption that its stable category has constructible cones with respect to the induced cluster-tilting object. This formula generalizes those obtained by Wang-Wei-Zhang for $\mathcal C$ in the one-dimensional case and by Keller-Plamondon-Qin for (stably) $2$-Calabi-Yau Frobenius or triangulated categories. As a consequence, we express the frozen term in an Auslander-Reiten mesh with the character of a minimal cosyzygy middle term. For acyclic quivers with principal coefficients, we compute these frozen multiplicities in Higgs categories and obtain explicit principal coefficient mesh relations.
Comments24 pages
