$M_{2}({\mathbb F})$上的$H$-模代数结构

$H$-Module Algebra Structures On $M_{2}({\mathbb F})$

中文关键词:  $H$-模代数  矩阵的平方根  Sweedler代数

英文关键词:$H$-module algebras  square root of matrix  Sweedler algebra

中文摘要:

      设${\mathbb F}$是特征为零的代数闭域, $H$为非点化非幺模的8维非半单Hopf代数, $M_{2}({\mathbb F})$为${\mathbb F}$上二阶方阵组成的全矩阵代数. 本文的主要目的是讨论和分类$M_{2}({\mathbb F})$上所有的$H$-模代数结构.

英文摘要:

      Let ${\mathbb F}$ be an algebraically closed field of characteristic $0$, $H$ be an eight-dimensional non-semisimple Hopf algebra which is neither pointed nor unimodular and $M_{2}({\mathbb F})$ be the full matrix algebra of $2\times 2$ over ${\mathbb F}$. In this paper, we discuss and classify all $H$-module algebra structures on $M_{2}({\mathbb F})$.