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
本文为斜对称化簇代数构造范畴模型与簇特征，证明良好性等价于非退化可实现性，并利用三角扩张与突变得到良好实现，进而定义满足突变的$F$-多项式并构造簇基。
AI 中文摘要
我们为承认良好分支实现的斜对称化簇代数构造了范畴模型和簇特征。良好性等价于非退化可实现性。当给定一个红化序列时，只需检查沿该序列的箭类型符号相干性。三角扩张在任意连接双模类型下保持良好性，当两个分量矩阵都承认红化序列时。因此，从单顶点通过三角扩张和突变得到的每个矩阵，对于每个相容的正整数对称化子，都承认一个良好的Jacobi有限非退化实现。对于良好的Jacobi有限非退化实现，表示格拉斯曼流形上驯服单值性的交替迹定义了满足无刚性假设的突变的$F$-多项式。在种子可达性条件下，每个完全初始序决定了具有任意几何系数（冻结变量取逆）的中簇代数的一个基。当中代数与上代数重合时，同一族是上簇代数基。对于固定的Jacobi代数和$\delta$-向量，一般单值性$F$-多项式的Newton多面体与序无关。
英文摘要
We construct categorical models and cluster characters for skew-symmetrizable cluster algebras admitting good ramified realizations. Goodness is equivalent to nondegenerate realizability. When a reddening sequence is given, it is enough to check sign coherence of the arrow types along that sequence. Triangular extensions with arbitrary connecting bimodule types preserve goodness when both component matrices admit reddening sequences. Consequently, every matrix obtained from one vertex by triangular extensions and mutations admits a good Jacobi-finite nondegenerate realization for every compatible positive integral symmetrizer. For a good Jacobi-finite nondegenerate realization, alternating traces of tame monodromy on representation Grassmannians define $F$-polynomials satisfying mutation without a rigidity hypothesis. Under the seed reachability condition, every full initial order determines a basis of the middle cluster algebra for arbitrary geometric coefficients, with frozen variables inverted. The same family is an upper-cluster-algebra basis when the middle and upper algebras coincide. For a fixed Jacobian algebra and $δ$-vector, the Newton polytope of the generic monodromy $F$-polynomial is independent of the order.
Comments88 pages, comments are welcome
