Annales Henri Poincaré

, Volume 16, Issue 7, pp 1689–1707 | Cite as

Generalizations of Poisson Structures Related to Rational Gaudin Model

  • Dimitri Gurevich
  • Vladimir Rubtsov
  • Pavel Saponov
  • Zoran ŠkodaEmail author


The Poisson structure arising in the Hamiltonian approach to the rational Gaudin model looks very similar to the so-called modified Reflection Equation Algebra. Motivated by this analogy, we realize a braiding of the mentioned Poisson structure, i.e. we introduce a “braided Poisson” algebra associated with an involutive solution to the quantum Yang–Baxter equation. Also, we exhibit another generalization of the Gaudin type Poisson structure by replacing the first derivative in the current parameter, entering the so-called local form of this structure, by a higher order derivative. Finally, we introduce a structure, which combines both generalizations. Some commutative families in the corresponding braided Poisson algebra are found.


Poisson Bracket Local Form Poisson Structure Leibniz Rule Poisson Algebra 
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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Dimitri Gurevich
    • 1
  • Vladimir Rubtsov
    • 2
    • 3
  • Pavel Saponov
    • 4
    • 5
  • Zoran Škoda
    • 6
    Email author
  1. 1.LAMAVUniversité de ValenciennesValenciennesFrance
  2. 2.UNAM, LAREMA UMR 6093 du CNRSUniversité d’AngersAngers, Cedex 01France
  3. 3.ITEP, Theory Division25, Bol.TcheremushkinskayaMoscowRussia
  4. 4.National Research University Higher School of EconomicsInternational Laboratory of Representation Theory and Mathematical PhysicsMoscowRussia
  5. 5.Institute for High Energy PhysicsMoscowRussia
  6. 6.Division of Theoretical PhysicsRudjer Bošković InstituteZagrebCroatia

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