经典型量子F多项式
Quantum F-polynomials in Classical Types
摘要：
在他们的“Cluster Algebras IV”论文中，Fomin和Zelevinsky定义了F-多项式和g-向量，他们证明了任何簇代数中的簇变量都可以用一个包含适当的F-多项式和g-向量的公式表示。在本文的前身“量子簇代数中的F-多项式”中，我们定义并证明了量子F-多项式的存在性，量子F-多项式是量子簇代数中F-多项式的类似物，在这个意义上，任何量子簇代数中的簇变量都可以用量子F-多项式和g-向量的类似公式表示。本文给出了初始交换矩阵为非循环矩阵时经典型簇代数的F-多项式和量子F-多项式的计算公式。
英文摘要：
In their "Cluster Algebras IV" paper, Fomin and Zelevinsky defined F-polynomials and g-vectors, and they showed that the cluster variables in any cluster algebra can be expressed in a formula involving the appropriate F-polynomial and g-vector. In "F-polynomials in Quantum Cluster Algebras," the predecessor to this paper, we defined and proved the existence of quantum F-polynomials, which are analogs of F-polynomials in quantum cluster algebras in the sense that cluster variables in any quantum cluster algebra can be expressed in a similar formula in terms of quantum F-polynomials and g-vectors. In this paper, we give formulas for both F-polynomials and quantum F-polynomials for cluster algebras of classical type when the initial exchange matrix is acyclic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
