p^r-李代数和幂零李代数的表示

p r -Lie Algebras and Reoresentations of Nilpotent Lie Algebras

给出了ｐｒ－李代数的定义，证明了ｐｒ－李代数具有许多与限制李代数类似的性质，然后利用ｐｒ－李代数概念，讨论了一般幂零李代数不可约表示的同构类，得到了特征标为Ｓ的不可约表示同构类的个数。

In this note,the p r -Lie algebra is defined.We show that the p r -Lie algebra has many similar properties as the restricted Lie algebra has.With the concept of p r -Lie algebra,we explor the isomorphic classes of irreducible module of a nilpotent Lie algebra.We obtain the number of isomorphic classes of irreducible module with character S.Associating with results in ,we obtain some results about the graded modules of a graded Lie algebra.