Restricted one-dimensional central extensions of restricted simple Lie algebras

We study the restricted one-dimensional central extensions of an arbitrary finite dimensional restricted simple Lie algebra for p≥5p≥5. For H2(g)=0H2(g)=0, we explicitly describe the cocycles spanning H⁎2(g), and in the case H2(g)≠0H2(g)≠0, we give a procedure to describe a basis for H⁎2(g).