Compatible Lie brackets related to elliptic curve
Odesskii, A V ; Sokolov, V V
arXiv, 0506503 / Harvested from arXiv
Text on arXiv
For the direct sum of several copies of sl_n, a family of Lie brackets compatible with the initial one is constructed. The structure constants of these brackets are expressed in terms of theta-functions associated with an elliptic curve. The structure of Casimir elements for these brackets is investigated. A generalization of this construction to the case of vector-valued theta-functions is presented. The brackets define a multi-hamiltonian structure for the elliptic sl_n-Gaudin model. A different procedure for constructing compatible Lie brackets based on the argument shift method for quadratic Poisson brackets is discussed.
Publié le : 2005-06-24
Classification:  Mathematics - Quantum Algebra,  High Energy Physics - Theory,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  17B80, 17B63, 32L81, 14H70 
@article{0506503,
     author = {Odesskii, A V and Sokolov, V V},
     title = {Compatible Lie brackets related to elliptic curve},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506503}
}

Odesskii, A V; Sokolov, V V. Compatible Lie brackets related to elliptic curve. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506503/