| 关于Cartan矩阵的对称性 |
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| 引用本文： | 曾吉文.关于Cartan矩阵的对称性[J].厦门大学学报(自然科学版),1999,38(1):17-20. |
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| 作者姓名： | 曾吉文 |
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| 作者单位： | 厦门大学数学系,厦门,361005 |
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| 摘 要： | 给出非分裂域上的Ｃａｒｔａｎ矩阵对称的充分必要条件．对域Ｆ上的对称代数Ａ，通过考察其有关单模的自同态代数的维数，确定Ａ的Ｃａｒｔａｎ矩阵是否对称或置换对称（当Ａ为ｑｕａｓｉ－Ｆｒｏｂｅｎｉｕｓ代数）．
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| 关 键 词： | 代数，单模，Cartan矩阵 |
The Symmetry of Cartan Matrix |
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| Zeng Jiwen.The Symmetry of Cartan Matrix[J].Journal of Xiamen University(Natural Science),1999,38(1):17-20. |
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| Authors: | Zeng Jiwen |
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| Abstract: | Let A be a quasi Frobenius algebra over a field F and C=(C ij ) the Cartan matrix of A. Using endomorphism algebra of simple modules, the author gives a sufficient and necessary condition of C being symmetric or permutation symmetric, according to A as a symmetric algebra or a quasi Frobenius algebra. Specially when F is a splitting field of A, C is symmetric or permutation symmetric. |
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| Keywords: | Algebra Simple modules Cartan matrix |
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