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.
ON THE BIHAMILTONIAN STRUCTURE OF THE SUPERSYMMETRIC KDV HIERARCHIES - A LIE SUPERALGEBRAIC APPROACH / C. MOROSI, L. PIZZOCCHERO. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 158:2(1993), pp. 267-288. [10.1007/BF02108075]
ON THE BIHAMILTONIAN STRUCTURE OF THE SUPERSYMMETRIC KDV HIERARCHIES - A LIE SUPERALGEBRAIC APPROACH
L. PizzoccheroUltimo
1993
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.Pubblicazioni consigliate
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