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

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 module...

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Veröffentlicht in:Mathematics (Basel) Jg. 10; H. 10; S. 1728
Hauptverfasser: Dilxat, Munayim, Gao, Shoulan, Liu, Dong, Xia, Limeng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.05.2022
Schlagworte:
Algebra
Differential equations
Lie groups
Mathematical analysis
Mathematics
Modules
Operators (mathematics)
Quantum field theory
Tensors
ISSN:2227-7390, 2227-7390
Online-Zugang:Volltext
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Zusammenfassung: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.
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ObjectType-Feature-2
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ISSN:2227-7390
2227-7390
DOI:10.3390/math10101728