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Generalizations of Poisson Structures Related to Rational Gaudin Model

Abstract :

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.

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https://hal.archives-ouvertes.fr/hal-01392198
Contributor : Okina Université d'Angers <>
Submitted on : Friday, November 4, 2016 - 10:46:43 AM
Last modification on : Monday, March 9, 2020 - 6:15:55 PM

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Dimitri Gurevich, Vladimir Roubtsov, Pavel Saponov, Zoran Škoda. Generalizations of Poisson Structures Related to Rational Gaudin Model. Annales Henri Poincaré, Springer Verlag, 2015, 16 (7), pp.1689-1707. ⟨10.1007/s00023-014-0350-4⟩. ⟨hal-01392198⟩

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