<inline-formula><math display="inline"><semantics><mrow><mi>U</mi><mo>(</mo><mi mathvariant="fraktur">h</mi><mo>)</mo></mrow></semantics></math></inline-formula>-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(h)-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.

Keywords

• Virasoro algebra
• differential operator
• polynomial module
• Weyl algebra