Classical affine W-superalgebras via generalized Drinfeld-Sokolov reductions and related integrable systems
Mathematical Physics
2017-11-29 v1 math.MP
Rings and Algebras
Representation Theory
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 , 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.
Keywords
Cite
@article{arxiv.1711.06344,
title = {Classical affine W-superalgebras via generalized Drinfeld-Sokolov reductions and related integrable systems},
author = {Uhi Rinn Suh},
journal= {arXiv preprint arXiv:1711.06344},
year = {2017}
}