Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Drinfeld-Sokolov reduction on a simple lie algebra from the bihamiltonian point of view

  • 135 Accesses

  • 29 Citations


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 to check access.


  1. 1.

    DrinfeldV. G. and SokolovV. V., Lie algebras and equations of Korteweg-de Vries type, J. Soviet Math. 30, 1975–2063 (1985).

  2. 2.

    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).

  3. 3.

    MarsdenJ. E. and RatiuT., Reduction of Poisson manifolds, Lett. Math. Phys. 11, 161–169 (1986).

  4. 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, Università di Milano.

  5. 5.

    KostantB., Lie group representations on polynomial rings, Amer. J. Math. 85, 327–404 (1963).

  6. 6.

    SerreJ-P., Complex Semisimple Lie Algebras, Springer-Verlag, New York, 1987.

  7. 7.

    KostantB., The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81, 973–1032 (1959).

Download references

Author information

Additional information

This work has been supported by the Italian MURST and by the GNFM of the Italian C.N.R.

Rights and permissions

Reprints 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

Download citation

Mathematics Subject Classifications (1991)

  • Primary: 58F07
  • Secondary: 35Q53