| 高凤霞,杨士林.3阶全矩阵代数的H8-模代数结构[J].数学年刊A辑,2017,38(2):215~226 |
| 3阶全矩阵代数的H8-模代数结构 |
| The H8-Module Algebra Structures on M3(\C) |
| Received:February 06, 2015 Revised:September 28, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0017 |
| 中文关键词: Full matrix algebra, Weak similarity, Module algebra |
| 英文关键词:Full matrix algebra, Weak similarity, Module algebra |
| 基金项目:本文受到国家自然科学基金(No.11471186,No.11671024)和北京市自然科学基金(No.1162002)的资助. |
| Author Name | Affiliation | E-mail | | GAO Fengxia | College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
Basic Department, Henan Institute of Technology, Xinxiang 453003, Henan, China. | gaofengxiahappy@163.com | | YANG Shilin | Corresponding author. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China. | slyang@bjut.edu.cn |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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