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. Pizzocchero
Ultimo
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.
supersymmetric soliton equations ; supermanifolds ; biHamiltonian structures ; Lie superalgebras
Settore MAT/07 - Fisica Matematica
Settore MAT/03 - Geometria
1993
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/189458
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 19
  • ???jsp.display-item.citation.isi??? 18
social impact