Quantisations of the Volterra hierarchy

DOI10.1007/s11005-022-01588-1OpenAlexW4296252077MaRDI QIDQ2079262

Sylvain Carpentier, Jing Ping Wang, Alexander V. Mikhailov

Publication date: 29 September 2022

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.03095

zbMATH Keywords

superintegrable systemsquantum integrabilitynon-deformation quantisationquantised algebraquantum Volterra equation

Mathematics Subject Classification ID

Groups and algebras in quantum theory and relations with integrable systems (81R12) Geometry and quantization, symplectic methods (81S10) Applications of Lie algebras and superalgebras to integrable systems (17B80) Deformation quantization, star products (53D55) Geometric quantization (53D50) Lattice dynamics; integrable lattice equations (37K60) Special quantum systems, such as solvable systems (81Q80) Canonical quantization (81S08) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37) Completely integrable discrete dynamical systems (37J70)

Uses Software

• Plural

Cites Work

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• Classification of Integrable One-Component Systems on Associative Algebras
• On some class of homogeneous polynomials and explicit form of integrable hierarchies of differential–difference equations
• On some class of reductions for the Itoh–Narita–Bogoyavlenskii lattice
• Algebraic constructions of integrable dynamical systems-extensions of the Volterra system
• The Hungry-Volterra Model – The Classical and Quantum Integrable Structures
• Recursion Operator of the Narita–Itoh–Bogoyavlensky Lattice
• Recursion and Hamiltonian operators for integrable nonabelian difference equations
• Quantisation ideals of nonabelian integrable systems

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