# ClassicalN=1W-superalgebras from Hamiltonian reduction

Research paper by José M. Figueroa-O'Farrill, Eduardo Ramos

Indexed on: 01 Mar '92Published on: 01 Mar '92Published in: Communications in Mathematical Physics

#### Abstract

A combinatorial proof is presented of the fact that the space of supersymmetric Lax operators admits a Poisson structure analogous to the second Gel'fand-Dickey bracket of the generalized KdV hierarchies. This allows us to prove that the space of Lax operators of odd order has a symplectic submanifold-defined by (anty)symmetric operators-which inherits a Poisson structure defining classicalW-superalgebras extending theN=1 supervirasoro algebra. This construction thus yields an infinite series of extended superconformal algebras.