J4 ›› 2013, Vol. 48 ›› Issue (8): 24-29.

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The module algebra structures on M2(k)

ZHAO Shi-yin1,2, ZHOU Ke-yuan1   

  1. 1. Department of Teachers Education, Suqian College, Suqian 223800, Jiangsu, China;
    2. School of Mathematical Science, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Received:2012-08-01 Online:2013-08-20 Published:2013-08-21

Abstract:

The equivalent classifications of some matrices and pairs of matrices with respect to the weak similarity are studied, respectively. Then by applying these results, the isomorphism classifications of kC2-module algebra structures and kC3module algebra structures on the full matrix algebra M2(k) are described. Finally, kS3module algebra structures on the full matrix algebra M2(k) are given up to isomorphism. When k is an algebraically closed filed, the isomorphism classifications of kS3module algebraic structures on the full matrix algebra M2(k) are obtained.

Key words: weak similarity; Hopf algebra; module algebra

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