Restricted Cohomology of Restricted Lie Superalgebras

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