Generalizations of Poisson structures related to rational Gaudin model (CROSBI ID 201035)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Gurevich, Dimitri ; Rubtsov, Vladimir ; Saponov, Pavel ; Škoda, Zoran
engleski
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.
Gaudin model ; Poisson structure ; (modified) Reflection Equation algebra ; braiding ; involutive symmetry ; Hecke symmetry
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Podaci o izdanju
16 (7)
2015.
1689-1707
objavljeno
1424-0637
1424-0661
10.1007/s00023-014-0350-4