一类四阶完全符号斜对称矩阵  

A class of totally sign-skew-symmetric 4×4 matrix

作　　者：牛效华 唐孝敏[1] NIU Xiaohua;TANG Xiaomin(School of Mathematical Sciences,Heilongjiang Univesity,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2024年第5期513-518,F0003,共7页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(12271085);黑龙江省自然科学基金资助项目(HL2020A020)。

摘　　要：丛代数通常由一个特定阶数的完全符号斜对称矩阵以及一组初始丛变量,通过突变关系来构建。值得注意的是,对于任意的循环型符号斜对称矩阵,它们并不一定满足完全符号斜对称的性质。本文专注于探讨一类特殊的四阶循环型符号斜对称矩阵,在矩阵的突变过程中,这类矩阵能够保持其类型不变,从而得到一类满足完全符号斜对称性质的矩阵。Cluster algebra is usually constructed by a totally signed skew-symmetric matrix of a specific order,together with a set of initial cluster variables,through mutation relations.It is worth noting that not all cyclic skew-symmetric matrices satisfy the totally skew-symmetric property.This article focuses on a specific class of fourth-order cyclic skew-symmetric matrices,which retain their type throughout the mutation process of the matrix,ultimately leading to a set of matrices that fully conform to the totally skew-symmetric property.

关 键 词：丛代数 符号斜对称矩阵 矩阵突变 完全符号斜对称 

分 类 号：O151.21[理学—数学]