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

Author

Listed:
  • 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
    Department of Mathematics, Huzhou University, Huzhou 313000, China)

  • Limeng Xia

    (Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, China)

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.

Suggested Citation

  • Munayim Dilxat & Shoulan Gao & Dong Liu & Limeng Xia, 2022. "U ( h ) -Free Modules over the Lie Algebras of Differential Operators," Mathematics, MDPI, vol. 10(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1728-:d:818400
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