$H$-Module Algebra Structures On $M_{2}({\mathbb F})$
Received:October 14, 2014  Revised:March 20, 2015
Key Word: $H$-module algebras   square root of matrix   Sweedler algebra
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11271043; 11471186).
 Author Name Affiliation Fengxia GAO College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China Shilin YANG College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China
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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 $M_{2}({\mathbb F})$.