Generalizations of Poisson Structures Related to Rational Gaudin Model

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TitreGeneralizations of Poisson Structures Related to Rational Gaudin Model
Type de publicationArticle de revue
AuteurGurevich, Dimitri, Roubtsov, Vladimir , Saponov, Pavel, Škoda, Zoran
PaysSuisse
EditeurSpringer Verlag
VilleBâle
TypeArticle scientifique dans une revue à comité de lecture
Année2015
LangueAnglais
DateJan-07-2015
Numéro7
Pagination1689–1707
Volume16
Titre de la revueAnnales Henri Poincaré
ISSN1424-0637
Mots-clés(modified) reflection equation algebra, braiding, Gaudin model, Hecke symmetry, involutive, Poisson structure, symmetry
Résumé en anglais

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.

URL de la noticehttp://okina.univ-angers.fr/publications/ua13632
DOI10.1007/s00023-014-0350-4
Titre abrégéAnn. Henri Poincaré