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Quantisations of the Volterra hierarchy

Carpentier, Sylvain, Mikhailov, Alexander V., Wang, Jing Ping (2022) Quantisations of the Volterra hierarchy. Letters in Mathematical Physics, 112 (5). Article Number 94. ISSN 0377-9017. (doi:10.1007/s11005-022-01588-1) (KAR id:96999)

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In this paper, we explore a recently emerged approach to the problem of quantisation based on the notion of quantisation ideals. We explicitly prove that the nonabelian Volterra together with the whole hierarchy of its symmetries admits a deformation quantisation. We show that all odd-degree symmetries of the Volterra hierarchy admit also a non-deformation quantisation. We discuss the quantisation problem for periodic Volterra hierarchy including their quantum Hamiltonians, central elements of the quantised algebras, and demonstrate super-integrability of the quantum systems obtained. We show that the Volterra system with period 3 admits a bi-quantum structure, which can be regarded as a quantum deformation of its classical bi-Hamiltonian structure.

Item Type: Article
DOI/Identification number: 10.1007/s11005-022-01588-1
Uncontrolled keywords: The quantum Volterra equation, Quantum integrability, Super integablesystems, Non-deformation quantisation, Quantised algebra
Subjects: Q Science
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: Engineering and Physical Sciences Research Council (
Depositing User: Jing Ping Wang
Date Deposited: 20 Sep 2022 09:43 UTC
Last Modified: 04 Jul 2023 13:27 UTC
Resource URI: (The current URI for this page, for reference purposes)
Wang, Jing Ping:
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