Cohomology groups of reduced enveloping algebras (Q803255)

The classification theory of irreducible modules of a restricted Lie algebra L of prime characteristic p leads naturally to the consideration of a family of associative algebras, the so called reduced enveloping algebras, u(L,S) where \(S\in L^*\). The article under review deals with the cohomology of u(L,S). The connection between the Hochschild cohomology of u(L,S) and that of the restricted enveloping algebra \(u(L):=u(L,0)\) is established. Various aspects of the interplay between the structural features of L and its restricted cohomology are investigated. For instance, some nonvanishing theorems for nilpotent and non-toral completely solvable algebras are obtained. Finally, the passage from the restricted to the ordinary cohomology groups of L by means of a Grothendieck spectral sequence is described.