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arXiv · 1312.7813

Generalizations of Poisson structures related to rational Gaudin model

Dimitri Gurevich·Vladimir Rubtsov·Pavel Saponov·Zoran Skoda
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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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Dimitri Gurevich, Vladimir Rubtsov, Pavel Saponov, Zoran Skoda. 2013-12-30. Generalizations of Poisson structures related to rational Gaudin model. https://arxiv.org/abs/1312.7813

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