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.
Titolo: | ON THE BIHAMILTONIAN STRUCTURE OF THE SUPERSYMMETRIC KDV HIERARCHIES - A LIE SUPERALGEBRAIC APPROACH |
Autori: | PIZZOCCHERO, LIVIO (Ultimo) |
Parole Chiave: | supersymmetric soliton equations ; supermanifolds ; biHamiltonian structures ; Lie superalgebras |
Settore Scientifico Disciplinare: | Settore MAT/07 - Fisica Matematica Settore MAT/03 - Geometria |
Data di pubblicazione: | 1993 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/BF02108075 |
Appare nelle tipologie: | 01 - Articolo su periodico |