Jacobian matrices of Y-seed mutations
Jacobian matrices of Y-seed mutations
复制标题
Y 种子突变的雅可比矩阵
DOI：
10.1016/j.aam.2019.101987
复制
发表时间：
2020
影响因子：
1.1
通讯作者：
Mizuno Yuma
中科院分区：
文献类型：
--
作者：
Yasukawa;K.;Kawarabata;C.;Tanaka;E.;Mimura;K.;Nakamura;K.;Fujinaga;K. and Kato;Y.;Mizuno Yuma;Mizuno Yuma
对于任意的突变序列，我们定义了一对矩阵，描述了从突变序列确定的聚类变换的不动点方程。我们给出了这对矩阵和簇变换的雅可比矩阵之间的显式关系。进一步证明了在一定的簇变量限制下，这种关系可归结为簇变换的矩阵对与簇变换的C-矩阵之间的关系。作为一个应用，我们证明了与一次穿刺表面颤抖没有最大的绿色或红化序列。
For any quiver mutation sequence, we define a pair of matrices that describe a fixed point equation of a cluster transformation determined from the mutation sequence. We give an explicit relationship between this pair of matrices and the Jacobian matrix of the cluster transformation. Furthermore, we show that this relationship reduces to a relationship between the pair of matrices and theC-matrix of the cluster transformation in a certain limit of cluster variables. As an application, we prove that quivers associated with once-punctured surfaces do not have maximal green or reddening sequences.