Irreducible modules over finite simple Lie pseudoalgebras IV. Non-primitive pseudoalgebras.

Let d \subset d' be finite-dimensional Lie algebras, H=U(d), H' = U(d') the corresponding universal enveloping algebras endowed with the canonical cocommutative Hopf algebra structure. We show that if L is a primitive Lie pseudoalgebra over H then all finite irreducible L' = Cur_H^{H'}-modules are of the form Cur_H^{H'} V , where V is an irreducible L-module, with a single class of exceptions. Indeed, when L=H(d, chi, omega), we introduce non-current L'-modules that are obtained by modifying the current pseudoaction with an extra term depending on an element t \in d' - d, which must satisfy some technical conditions. This, along with results from [2–4], completes the classification of finite irreducible modules of finite simple Lie pseudoalgebras over the universal enveloping algebra of a finite-dimensional Lie algebra.