Geodesic
Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 485-500

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We construct hierarchies of commutative Poisson subalgebras for Sklyanin brackets. Each of the subalgebras is generated by a complete set of integrals in involution. Some new integrable systems and schemes for separation of variables for them are elaborated using various well-known representations of the brackets. The constructed models include deformations for the Goryachev–Chaplygin top, the Toda chain, and the Heisenberg model.
Keywords: finite-dimensional integrable systems, Lax representation, separation of variables.
Mots-clés : $r$-matrix algebras 
@article{TMF_2002_133_3_a12,
     author = {V. V. Sokolov and A. V. Tsiganov},
     title = {Commutative {Poisson} {Subalgebras} for {Sklyanin} {Brackets} and {Deformations} of {Some} {Known} {Integrable} {Models}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {485--500},
     publisher = {mathdoc},
     volume = {133},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a12/}
}
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V. V. Sokolov; A. V. Tsiganov. Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 485-500. http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a12/