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

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.