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Communications in Mathematical Physics

, Volume 158, Issue 2, pp 267–288 | Cite as

On the biHamiltonian structure of the supersymmetric KdV hierarchies. A Lie superalgebraic approach

  • Carlo Morosi
  • Livio Pizzocchero
Article

Abstract

We give a Lie superalgebraic interpretation of the biHamiltonian structure of known supersymmetric KdV equations. We show that the loop algebra of a Lie superalgebra carries a natural Poisson pencil, and we subsequently deduce the biHamiltonian structure of the supersymmetric KdV hierarchies by applying to loop superalgebras an appropriate reduction technique. This construction can be regarded as a superextension of the Drinfeld-Sokolov method for building a KdV-type hierarchy from a simple Lie algebra.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Carlo Morosi
    • 1
  • Livio Pizzocchero
    • 2
    • 3
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanoItaly
  3. 3.Istituto Nazionale di Fisica NucleareItaly

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