Classical Affine W-Superalgebras via Generalized Drinfeld-Sokolov Reductions and Related Integrable Systems

Abstract

The purpose of this article is to investigate relations between W-superalgebras and integrable super-Hamiltonian systems. To this end, we introduce the generalized Drinfel'd-Sokolov (D-S) reduction associated to a Lie superalgebra and its even nilpotent element f, and we find a new definition of the classical affine W-superalgebra via the D-S reduction. This new construction allows us to find free generators of , as a differential superalgebra, and two independent Lie brackets on Moreover, we describe super-Hamiltonian systems with the Poisson vertex algebras theory. A W-superalgebra with certain properties can be understood as an underlying differential superalgebra of a series of integrable super-Hamiltonian systems.