Cohomology And Nullcones Of Jacobson-Witt Algebras

Let L =(?)(n; m) be the Jacobson-Witt algebra over the algebraic closed field with the characteristic p > 0. The aim of this paper is to compute the cohomology of L over the divided power algebra (p ≥ max{3n - 3,5}, which implies that p > n + 1) and the trivial module K (the latter one is to get the theorem that the result is zero and p only need to be bigger than 2) At the same time, by the method of spectral sequence, we construct the relationship between the restricted cohomology of L = W(n; 1) over the divided power algebra and the coordinate algebra of the nullcone of W(n; 1).