Classical R-Matrices and the Feigin-Odesskii Algebra via Hamiltonian and Poisson Reductions
Braden, H. W. ; Dolgushev, V. A. ; Olshanetsky, M. A. ; Zotov, A. V.
arXiv, 0301121 / Harvested from arXiv
Text on arXiv
We present a formula for a classical $r$-matrix of an integrable system obtained by Hamiltonian reduction of some free field theories using pure gauge symmetries. The framework of the reduction is restricted only by the assumption that the respective gauge transformations are Lie group ones. Our formula is in terms of Dirac brackets, and some new observations on these brackets are made. We apply our method to derive a classical $r$-matrix for the elliptic Calogero-Moser system with spin starting from the Higgs bundle over an elliptic curve with marked points. In the paper we also derive a classical Feigin-Odesskii algebra by a Poisson reduction of some modification of the Higgs bundle over an elliptic curve. This allows us to include integrable lattice models in a Hitchin type construction.
Publié le : 2003-01-17
Classification:  High Energy Physics - Theory,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0301121,
     author = {Braden, H. W. and Dolgushev, V. A. and Olshanetsky, M. A. and Zotov, A. V.},
     title = {Classical R-Matrices and the Feigin-Odesskii Algebra via Hamiltonian and
  Poisson Reductions},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0301121}
}

Braden, H. W.; Dolgushev, V. A.; Olshanetsky, M. A.; Zotov, A. V. Classical R-Matrices and the Feigin-Odesskii Algebra via Hamiltonian and
  Poisson Reductions. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0301121/