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

AbstractGiven a Lie algebra g of Cartan type we construct an infinite-dimensional cocommutative Hopf algebraD(G)u(g) which is the analog of the distribution algebra of a connected reductive algebraic group. We show that the simpleu(g)-modules lift to aD(G)u(g)-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(g)-modules are computed by using these algebraic group techniques