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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (10): 46-51.doi: 10.6040/j.issn.1671-9352.0.2020.256

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自内射Nakayama代数的q-Cartan矩阵

赵跳,章超*   

  1. 贵州大学数学与统计学院, 贵州 贵阳 550025
  • 出版日期:2020-10-20 发布日期:2020-10-07
  • 作者简介:赵跳(1995— ), 男, 硕士研究生, 研究方向为代数表示论. E-mail:1475759283@qq.com*通信作者简介:章超(1986— ), 男,博士, 教授, 研究方向为代数表示理论. E-mail:zhangc@amss.ac.cn
  • 基金资助:
    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)

q-Cartan matrices of self-injective Nakayama algebras

ZHAO Tiao, ZHANG Chao*   

  1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China
  • Online:2020-10-20 Published:2020-10-07

摘要: 证明了任意自内射的Nakayama代数Aq-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-(qn)m)/(1-qn),〓〓〓如果(n,m)=1;((1-q[m,n])(m,n))/(1-qn),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。

关键词: Cartan行列式, 可对角化矩阵, 循环矩阵

Abstract: 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-(qn)m)/(1-qn), if(n,m)=1;((1-q[m,n])(m,n))/(1-qn),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.

Key words: Cartan determinant, diagonalizable matrix, circulant matrix

中图分类号: 

  • O153.3
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