Super-affine hierarchies and their Poisson embeddings

  • Francesco Toppan
Supersymmetric Quantum Mechanics And Integrable Systems
Part of the Lecture Notes in Physics book series (LNP, volume 524)


The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for constructing matrix-type Lax operators, which makes the supersymmetric case essentially different from the bosonic counterpart, is overcome via the notion of Poisson embeddings (P.E.), i.e. Poisson mappings relating affine structures to conformal structures (in their simplest version P.E. coincide with the Sugawara construction). A full class of hierarchies can be recovered by using uniquely Lie-algebraic notions. The group-algebraic properties implicit in the super-affine picture allow a systematic derivation of reduced hierarchies by imposing either coset conditions or hamiltonian constraints (or possibly both).


Poisson Bracket Conformal Algebra Supersymmetric Extension Integrable Hierarchy Hamiltonian Reduction 
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Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Francesco Toppan
    • 1
  1. 1.UFES, CCE Depto de FísicaVitória (ES)Brasil

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