We give a Lie superalgebraic interpretation of the biHamiltonian structure of the known susy KdV equations. We show that he loop algebra of a Lie superalgebra carries a natural Poisson pencil, and we subsequently deduce the biHamiltonian structure of the susy 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.
On the biHamiltonian structure of the supersymmetric KdV hierarchies. A Lie superalgebraic approach
MOROSI, CARLO;
1993-01-01
Abstract
We give a Lie superalgebraic interpretation of the biHamiltonian structure of the known susy KdV equations. We show that he loop algebra of a Lie superalgebra carries a natural Poisson pencil, and we subsequently deduce the biHamiltonian structure of the susy 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.File in questo prodotto:
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