3阶全矩阵代数的H8-模代数结构
The H8-Module Algebra Structures on M3(\C)

设$H_8$是非交换非余交换的8维半单Hopf代数, $\C[\K_4]$ 是克莱因四元群的群代数, $M_{3}(\C)$ 是复数域上的3阶全矩阵代数. 通过方阵和方阵对的弱相似给出了同构意义下 $M_{3}(\C)$上全部的$\C[\K_4]${-}模代数结构. 在此基础上结合 $H_8$与 $\C[\K_4]$ 的关系, 刻划了同构意义下$M_{3}(\C)$ 上所有的$H_8${-}模代数结构.
Let $H_8$ be the unique non-commutative and non-cocommutative 8-dimensional semi-simple Hopf algebra, $\C[\K_4]$ be the group algebra of Klein-4 group. By the definitions of weak similarity and square root of the matrix, the authors describe and classify all $\C[\K_4]$-module algebra structures on $M_{3}(\C)$. Then combining the relation between $H_8$ and $\C[\K_4]$, the authors give all $H_8$-module algebra structures on $M_{3}(\C)$ up to isomorphism.