| 自内射Nakayama代数的q-Cartan矩阵 |
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| 引用本文： | 赵跳,章超.自内射Nakayama代数的q-Cartan矩阵[J].山东大学学报(理学版),2020,55(10):46-51. |
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| 作者姓名： | 赵跳 章超 |
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| 作者单位： | 贵州大学数学与统计学院,贵州 贵阳550025 |
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| 基金项目： | 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) |
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| 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-(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。
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| 关 键 词： | Cartan行列式 可对角化矩阵 循环矩阵 |
q-Cartan matrices of self-injective Nakayama algebras |
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| ZHAO Tiao,ZHANG Chao.q-Cartan matrices of self-injective Nakayama algebras[J].Journal of Shandong University,2020,55(10):46-51. |
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| Authors: | ZHAO Tiao ZHANG Chao |
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| Institution: | School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China |
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| 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. |
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| Keywords: | Cartan determinant diagonalizable matrix circulant matrix |
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