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

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.