自内射Nakayama代数的q- Cartan矩阵  

q-Cartan matrices of self-injective Nakayama algebras

作　　者：赵跳 章超 ZHAO Tiao;ZHANG Chao(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,Guizhou,China)

机构地区：[1]贵州大学数学与统计学院,贵州贵阳550025

出　　处：《山东大学学报（理学版）》2020年第10期46-51,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11961007);贵州省科技厅项目(黔科合基础[2020]1Y405)。

摘　　要：证明了任意自内射的Nakayama代数A的q-Cartan矩阵CA(q)相似于一个对角矩阵,而且CA(q)的行列式为|CA(q)|={(1-(q^n)^m)/(1-q^n),如果(n,m)=1;((1-q[m,n])^(m,n))/(1-q^n),如果(n,m)≠1,其中n为单模的个数,m为齐次关系理想I中最短路径的长度,(n,m)表示n与m的最大公因数,[n,m]表示n与m的最小公倍数。The present paper mainly proves that the q-Cartan matrix of any self-injective Nakayama algebra A is diagonalizable and the determinant of q-Cartan|CA(q)|={(1-(q^n)m)/(1-q^n),if(n,m)=1;((1-q[m,n])^(m,n))/(1-q^n),if(n,m)≠1,where n is the number of simple modules,m is the length of the shortest paths in the homogeneous ideal I,and(n,m)is the greatest common divisor of n and m,[n,m]is the least common multiple of n and m.

关 键 词：Cartan行列式 可对角化矩阵 循环矩阵 

分 类 号：O153.3[理学—数学] O154.2[理学—基础数学]