二阶全矩阵代数的模代数结构

J4 ›› 2013, Vol. 48 ›› Issue (8): 24-29.

二阶全矩阵代数的模代数结构

赵士银1,2,周克元1

1.宿迁学院教师教育系, 江苏宿迁 223800; 2. 扬州大学数学科学学院, 江苏扬州 225002

收稿日期:2012-08-01 出版日期:2013-08-20 发布日期:2013-08-21
作者简介:赵士银(1978- ),男,硕士,讲师,研究方向为Hopf代数及量子群. Email:zsy2017@sina.com
基金资助:
国家自然科学基金资助项目(11171291);江苏省教育厅青蓝工程资助项目;宿迁学院自然科学基金项目(2012KY08)

The module algebra structures on M2(k)

ZHAO Shi-yin1,2, ZHOU Ke-yuan1

1. Department of Teachers Education, Suqian College, Suqian 223800, Jiangsu, China;
2. School of Mathematical Science, Yangzhou University, Yangzhou 225002, Jiangsu, China

Received:2012-08-01 Online:2013-08-20 Published:2013-08-21

摘要/Abstract

摘要：

研究了某些二阶矩阵及其二阶矩阵对关于弱相似关系的等价分类,讨论了二阶全矩阵代数的kC2-模代数结构和kC3-模代数结构的同构类。在同构意义下给出了二阶全矩阵代数的kS3-模代数结构,且当k为代数闭域时,得到了二阶全矩阵代数的kS3模代数结构的同构分类。

关键词: 弱相似; Hopf 代数;模代数

Abstract:

The equivalent classifications of some matrices and pairs of matrices with respect to the weak similarity are studied, respectively. Then by applying these results, the isomorphism classifications of kC2-module algebra structures and kC3module algebra structures on the full matrix algebra M2(k) are described. Finally, kS3module algebra structures on the full matrix algebra M2(k) are given up to isomorphism. When k is an algebraically closed filed, the isomorphism classifications of kS3module algebraic structures on the full matrix algebra M2(k) are obtained.

Key words: weak similarity; Hopf algebra; module algebra

赵士银1,2,周克元1. 二阶全矩阵代数的模代数结构[J]. J4, 2013, 48(8): 24-29.

ZHAO Shi-yin1,2, ZHOU Ke-yuan1. The module algebra structures on M2(k)[J]. J4, 2013, 48(8): 24-29.

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