Restricted Cohomology of Restricted Lie Superalgebras

Suppose the ground field F is an algebraically closed field characteristic of p > 2. In this paper, we investigate the restricted cohomology theory of restricted Lie superalgebras. Algebraic interpretations of low dimensional restricted cohomology of restricted Lie superalgebra are given. We show that there is a family of restricted model filiform Lie superalgebra L-p,p(lambda) structures parameterized by elements lambda is an element of F-p. We explicitly describe both the 1-dimensional ordinary and restricted cohomology superspaces of L. p,p with coefficients in the 1-dimensional trivial module and show that these superspaces are equal. We also describe the 2-dimensional ordinary and restricted cohomology superspaces of L-p,p(lambda) with coefficients in the 1-dimensional trivial module and show that these superspaces are unequal.