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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Bibliographic Details
Published in:Mathematics (Basel) Vol. 10; no. 10; p. 1728
Main Authors: Dilxat, Munayim, Gao, Shoulan, Liu, Dong, Xia, Limeng
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2022
Subjects:
Algebra
Differential equations
Lie groups
Mathematical analysis
Mathematics
Modules
Operators (mathematics)
Quantum field theory
Tensors
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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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ISSN:2227-7390
2227-7390
DOI:10.3390/math10101728