×

zbMATH — the first resource for mathematics

Drinfeld-Sokolov reduction on a simple Lie algebra from the bihamiltonian point of view. (English) Zbl 0767.58019
This paper is a part of a project of F. Magri’s group, aiming to frame all the properties of soliton equations in the theory of bihamiltonian systems. It is shown that the Drinfeld-Sobolev reduction is a particular case of a reduction process for Poisson manifolds suggested by Marsden and Ratiu.

MSC:
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DrinfeldV. G. and SokolovV. V., Lie algebras and equations of Korteweg-de Vries type, J. Soviet Math. 30, 1975-2063 (1985). · Zbl 0578.58040
[2] Casati, P., Magri, F., and Pedroni, M., Bihamiltonian manifolds and ?-function, Proc. 1991 Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory (M. J. Gotay, J. E. Marsden, and V. E. Moncrief, eds.) (to appear). · Zbl 0791.58050
[3] MarsdenJ. E. and RatiuT., Reduction of Poisson manifolds, Lett. Math. Phys. 11, 161-169 (1986). · Zbl 0602.58016
[4] Magri, F. and Morosi, C., A geometrical charactization of integrable Hamiltonian systems through the theory of Poisson-Nijenhuis manifolds, Quaderno S/19, Dipartimento di Matematica, Universit? di Milano.
[5] KostantB., Lie group representations on polynomial rings, Amer. J. Math. 85, 327-404 (1963). · Zbl 0124.26802
[6] SerreJ-P., Complex Semisimple Lie Algebras, Springer-Verlag, New York, 1987.
[7] KostantB., The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81, 973-1032 (1959). · Zbl 0099.25603
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.