线性序集Ringel对偶代数的Cartan矩阵  

Cartan matrices of Ringel dual algebras associated to linearly ordered sets

作　　者：张跃辉[1] 郭金萍[1] 

机构地区：[1]天津工程师范学院数学研究所,天津300222

出　　处：《天津工程师范学院学报》2006年第2期12-15,共4页Journal of Tianji University of Technology and Education

基　　金：国家自然科学基金资助项目(10371101)

摘　　要：设A且是线性序集{1<2<…<n-1<n}的对偶扩张代数,Γ=EndAT是A的Ringel对偶代数,则A的Cartan 矩阵的顺序主子式依次为,n,n-1,…,2,1,其逆序主子式均为1,而Γ的Cartan矩阵的顺序主子式均为1。进一步,A的Cartan矩阵的逆矩阵为三对角M-矩阵,其顺序主子式均为1。Let A be the dual extension algebra of the linearly ordered set {1〈2〈...〈n-1〈n } and Г = EndA T the Ringel dual of A. Then all the upper-left submatrices of the Cartan matrix of A have determinants n, n - 1 ,... ,2,1 in order, all the lower-right submatrices of the Cartan matrix of A have determinants 1 ; while all the upper-left submatriees of the Cartan matrix of Г have determinants 1. Moreover, the inverse of the Caftan matrix of A is a tridiagonal M-matrix with determinants of all the upper-left submatrices 1.

关 键 词：对偶扩张代数 Ringel对偶 CARTAN矩阵 Cartan行列式 

分 类 号：O152.21[理学—数学]