\(N\)-dimensional classical integrable systems from Hopf algebras

DOI10.1007/BF01690329zbMath0952.37022OpenAlexW2069121534MaRDI QIDQ1589229

M. Corsetti, Orlando Ragnisco, Ángel Ballesteros

Publication date: 7 December 2000

Published in: Czechoslovak Journal of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01690329

zbMATH Keywords

quantum algebrasCasimir elementGaudin system\(N\)-body integrable systemsintegrable quantum deformationphase space realizationsPoisson-Hopf symmetriesuniversal enveloping Hopf algebras

Mathematics Subject Classification ID

Related Items (12)

Universal chain structure of quadratic algebras for superintegrable systems with coalgebra symmetry ⋮ Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras ⋮ Embedding of the Racah algebra \(R(n)\) and superintegrability ⋮ Gaudin models with \(\mathcal U_q(\mathfrak{osp}(1|2))\) symmetry ⋮ Coalgebra symmetry for discrete systems ⋮ Two-Photon Algebra and Integrable Hamiltonian Systems ⋮ Exact solution of the quantum Calogero–Gaudin system and of its q deformation ⋮ Exact solution to a supersymmetric Gaudin model ⋮ SYMMETRY, INTEGRABILITY AND DEFORMATIONS OF LONG-RANGE INTERACTING HAMILTONIANS ⋮ LIE–HAMILTON SYSTEMS: THEORY AND APPLICATIONS ⋮ Poisson–Hopf deformations of Lie–Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra ⋮ Racah algebra R(n) from coalgebraic structures and chains of R(3) substructures

Cites Work

• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Über die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallgemeinerungen
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