The Discussion of P-envelope of Restricted Lie Superalgebra

Using the newdefinition restricted Lie superalgebra,this paper gives some results of P-envelope of Lie superalgeˉbra:first,each Lie superalgebra L has a universal P-envelope;second,suppose is a P-envelope of Lie superalgebra L and is a graded representation of Lamong which Vis-graded vector space,there exists a graded representation with p as the extenˉsion of p and each graded L-submodule of V as a graded G-submodule;third,for every restricted Lie superalgebra there is a S-reduced universal enveloping algebra of L.