U(h)-Free Modules over the Lie Algebras of Differential Operators

Abstract

This paper mainly considers a class of non-weight modules over the Lie algebra of the Weyl type. First, we construct the $U\left(\mathfrak{h}\right)$-free modules of rank one over the differential operator algebra. Then, we characterize the tensor products of these kind of modules and the quasi-finite highest weight modules. Finally, we undertake such research for the differential operator algebra of multi-variables.