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

Munayim Dilxat, Shoulan Gao, Dong Liu and Limeng Xia
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Munayim Dilxat: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Shoulan Gao: Department of Mathematics, Huzhou University, Huzhou 313000, China
Dong Liu: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Limeng Xia: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, China

Mathematics, 2022, vol. 10, issue 10, 1-12

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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