On Cohomology of Simple Modules for Modular Classical Lie Algebras

Abstract

In this article, we obtain some cohomology of classical Lie algebras over an algebraically closed field of characteristic p > h, where h is a Coxeter number, with coefficients in simple modules. We assume that these classical Lie algebras are Lie algebras of semisimple and simply connected algebraic groups. To describe the cohomology of simple modules, we will use the properties of the connections between ordinary and restricted cohomology of restricted Lie algebras.