Cohomology of graded Lie algebras of Cartan type of characteristic p
Let F be an algebraically closed field of characteristic \(p>3\) and \(L=\oplus_{i\geq -1}L_{[i]}^ a \)graded Lie algebra of Cartan type over F. For every irreducible \(L_{[0]}\)-module \(V_ 0\) a graded L- module \(\tilde V_ 0\) can be constructed from the tensor product of \(V_ 0\) and the appropriate subalgebra of a divided power algebra. The authors determine the structures of \(H^ 1(L,\tilde V_ 0)\) for \(L=W(2,{\mathfrak m})\), \(W(3,{\mathfrak m})\), or \(H(2,{\mathfrak m})\) and of \(H^ 1_*(L,V)\), where L is any restricted algebra from the above list, and V is an irreducible restricted L-module.
scientific article; zbMATH DE number 4036030