Algebraic Group Actions in the Cohomology Theory of Lie Algebras of Cartan Type Original Research Article

Given a Lie algebra image of Cartan type we construct an infinite-dimensional cocommutative Hopf algebraD(G)u(image) which is the analog of the distribution algebra of a connected reductive algebraic group. We show that the simpleu(image)-modules lift to aD(G)u(image)-structure. This additional structure is used to formulate and prove relative projectivity theorems for Lie algebras of Cartan type. The support varieties of certainD(G)u(image)-modules are computed by using these algebraic group techniques.