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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 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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00931978
Contributor : Vladimir Roubtsov Connect in order to contact the contributor
Submitted on : Thursday, January 16, 2014 - 10:34:04 AM
Last modification on : Wednesday, October 20, 2021 - 3:18:44 AM

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

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Dimitri Gurevich, Vladimir Rubtsov, Pavel Saponov, Zoran Skoda. Generalizations of Poisson structures related to rational Gaudin model. 2013. ⟨hal-00931978⟩

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