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.

Type de document :
Article dans une revue
Annales Henri Poincaré, Springer Verlag, 2015, 16 (7), pp.1689-1707. 〈10.1007/s00023-014-0350-4〉
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https://hal.archives-ouvertes.fr/hal-01392198
Contributeur : Okina Université d'Angers <>
Soumis le : vendredi 4 novembre 2016 - 10:46:43
Dernière modification le : lundi 5 février 2018 - 15:00:03

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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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