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Mikhailov, A. orcid.org/0000-0003-4238-6995 and Skrypnyk, T. (2024) Zhukovsky-Volterra top and quantisation ideals. [Preprint - arXiv]
Abstract
In this letter, we revisit the quantisation problem for a fundamental model of classical mechanics—the Zhukovsky-Volterra top. We have discovered a four-parametric pencil of compatible Poisson brackets, comprising two quadratic and two linear Poisson brackets. Using the quantisation ideal method, we have identified two distinct quantisations of the Zhukovsky-Volterra top. The first type corresponds to the universal enveloping algebras of so(3), leading to Lie-Poisson brackets in the classical limit. The second type can be regarded as a quantisation of the four-parametric inhomogeneous quadratic Poisson pencil. We discuss the relationships between the quantisations obtained in our paper, Sklyanin’s quantisation of the Euler top, and Levin-Olshanetsky-Zotov’s quantisation of the Zhukovsky-Volterra top.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an open access preprint under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | quantum top, quantisation ideal, quadratic Poisson brackets, Sklyanin algebra |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Dec 2024 13:10 |
Last Modified: | 17 Dec 2024 13:10 |
Published Version: | https://arxiv.org/abs/2405.16532 |
Identification Number: | 10.48550/arXiv.2405.16532 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:220900 |
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