Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalizations of Poisson structures related to rational Gaudin model   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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The categories of this paper are: atom-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph