特征2上Special代数S(3,1)的极小权向量

Minimal Weight Vectors for the Special Algebra S(3,1) in Characteristic 2

摘要: 通过研究李代数的既约包络代数的极小左理想来研究李代数的不可约模,通过确定生成极小左理想的极大权向量来确定不可约模,给出了特征p=2上的Special代数S(3,1)的特征标χ的高度为0的不可约模和它们的维数.

Abstract: The irreducible modules over a restricted Lie algebra are studied by determining the minimal left ideals of reduced enveloping algebra of the restricted Lie algebra.By constructing the maximal weight vectors which generate the mininal left ideals,irreducible L-modules with character height 0 are realized and their dimensions are given for the special algebra L=S(3,1) over an algebraically closed field of characteristic 2.