On the biHamiltonian structure of the supersymmetric KdV hierarchies. A Lie superalgebraic approach |
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| Authors: | Carlo Morosi Livio Pizzocchero |
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| Institution: | (1) Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano, Italy;(2) Dipartimento di Matematica, Università di Milano, Via C. Saldini 50, I-20133 Milano, Italy;(3) Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Italy |
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| 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. |
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