Homology Of Linear Lie Superalgebras

In this paper,we study the low-dimensional restricted cohomology of restricted Filiform Lie superalgebra with coefficients in the 1-dimensional trivial module on the field of the characteristic p>3.First,we give the restricted cochain complex and restricted coboundary operator of the restricted Filiform Lie superalgebra with coefficients in the 1-dimensional trivial module.Then,we describe the 1,2-dimensional restricted cohomology of the restricted Lie superalgebra with coefficients in the 1-dimensional trivial module,and give the corresponding dimension.Finally,we study the（restricted）superderivations of the restricted Filiform Lie superalgebra and give the 1-dimensional restricted cohomology of the restricted Filiform Lie superalgebra with coefficients in the adjoint module.