A duality theorem for hope module algebras over dedekind rings

Let L be a graded Lie algebra of Cartan type over an algebraically closed field of characteristic p≧3, which has been proved to be generalized restricted in the sense of [Shul, Shu2]. For a generalized restricted L-module M, the homological support variety ‖L‖_M is defined to be that of the primitive p-envelope P{L). A realization L of P(L) is given in Der(&;(m : n)). Furthermore, a class of generalized restricted highest weight L-modules lift to Dist(Tx)V(p)-module structures and their support varieties can be computed by using algebraic group techniques developed in [LN].