二阶全矩阵代数的二面体群模代数结构  

The module algebra structures of dihedral groups on the full matrix algebra of 2×2

作　　者：苏冬 SU Dong(School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471023,Henan,China)

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471023

出　　处：《山东大学学报（理学版）》2024年第2期14-21,31,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12201187);河南省自然科学基金资助项目(222300420156)。

摘　　要：利用矩阵弱相似及矩阵对弱相似的相关理论,在复数域C上,研究二阶全矩阵代数M_(2)(C)上m阶循环群C_(m)的模代数结构,并且在同构意义下刻画M_(2)(C)上所有的2m阶二面体群D_(2m)-模代数结构。By using the theories of weak similarity of matrices and weak similarity of matrix pairs,the module algebra structures of cyclic groups of C_(m) are researched over the full matrix algebra of 2×2 on the complex field C,and all module algebra structures of dihedral groups D_(2m) are characterized over the full matrix algebra of 2×2 up to isomorphism.

关 键 词：全矩阵代数 二面体群 弱相似 模代数 

分 类 号：O153.3[理学—数学]