Abstract
We show that the Drinfeld-Sokolov reduction can be framed in the general theory of bihamiltonian manifolds, with the help of a specialized version of a reduction theorem for Poisson manifolds by Marsden and Ratiu.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
DrinfeldV. G. and SokolovV. V., Lie algebras and equations of Korteweg-de Vries type, J. Soviet Math. 30, 1975–2063 (1985).
Casati, P., Magri, F., and Pedroni, M., Bihamiltonian manifolds and τ-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).
MarsdenJ. E. and RatiuT., Reduction of Poisson manifolds, Lett. Math. Phys. 11, 161–169 (1986).
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, Università di Milano.
KostantB., Lie group representations on polynomial rings, Amer. J. Math. 85, 327–404 (1963).
SerreJ-P., Complex Semisimple Lie Algebras, Springer-Verlag, New York, 1987.
KostantB., The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81, 973–1032 (1959).
Author information
Authors and Affiliations
Additional information
This work has been supported by the Italian MURST and by the GNFM of the Italian C.N.R.
Rights and permissions
About this article
Cite this article
Casati, P., Pedroni, M. Drinfeld-Sokolov reduction on a simple lie algebra from the bihamiltonian point of view. Lett Math Phys 25, 89–101 (1992). https://doi.org/10.1007/BF00398305
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00398305