The Affine Group Probability A_p Said That With The Power Of Zero Matrix

The representations of an affine group scheme is one of the basic research in the modern core mathematics. The discussion of such content needs many branches in algebra or other mathematicals. In general, the modern mathematical research for the affine group is based on abstract theory, is there a more intuitive approach to the research?In fact, the representations can be given by the nilpotent linear transformations with some conditions. From the correspondence between the nilpotent matrix and the hopf algebra homomorphism, we transform the representations of an affine group scheme into the problem of nilpotent matrixes, the study is transformed into concrete calculations.The main work in this paper is to show the relations between the abstract theory and the matrix calculation. This article not only gives the relationships between the representations and the nilpotent linear transformations, but also indicates the corresponding of the nilpotent matrix and the hopf algebra homomorphism. Further more we get the specific algorithms and procedures of calculating low-level nilpotent matrixes with prime characteristics. The results of calculations make the classification with the representations of the affine group scheme sense.