On the cohomology of the Jacobson–Witt algebra

Abstract

The investigating cohomology of the classical modular Lie algebras by using the methods of representation theory of algebraic groups allows to get a lot of interesting results. Now this trend observed in the studying cohomology of the Lie algebras of Cartan type in which results lead to study the cohomology of certain reductive groups. In this paper we give a complete description the cohomology of the Jacobson-Witt algebra W₃(1) over an algebraical closed field k of characteristic p > 3 with coefficients in the divided power algebra O₃(1) by calculating the cohomology of the classical Lie algebra sl₃(k):