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