# 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 modi?ed 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 ?rst 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 :
Pré-publication, Document de travail
LATEX, 16 pp. 2013

https://hal.archives-ouvertes.fr/hal-00931978
Soumis le : jeudi 16 janvier 2014 - 10:34:04
Dernière modification le : mercredi 19 décembre 2018 - 14:08:04

### Identifiants

• HAL Id : hal-00931978, version 1
• ARXIV : 1312.7813

### Citation

Dimitri Gurevich, Vladimir Rubtsov, Pavel Saponov, Zoran Skoda. Generalizations of Poisson structures related to rational Gaudin model. LATEX, 16 pp. 2013. 〈hal-00931978〉

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