Bavula, V.V. and Lu, T. (2017) Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules. Journal of Mathematical Physics, 58 (1). 011701. ISSN 0022-2488
Abstract
A classification of the simple weight modules is given for the (6-dimensional) Euclidean Lie algebra e(3) = sl2 nV3. As an intermediate step, a classification of all simple modules is given for the centralizer C of the Cartan element H (in the universal enveloping algebra U = U(e(3))). Generators and defining relations for the algebra C are found (there are three quadratic relations and one cubic relation). The algebra C is a Noetherian domain of Gelfand-Kirillov dimension 5. Classifications of prime, primitive, completely prime, and maximal ideals are given for the algebra U.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 AIP Publishing. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Nov 2017 16:04 |
Last Modified: | 01 Feb 2018 01:39 |
Published Version: | https://doi.org/10.1063/1.4973378 |
Status: | Published |
Publisher: | AIP Publishing |
Refereed: | Yes |
Identification Number: | 10.1063/1.4973378 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:124134 |