English

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 gg and its even nilpotent element ff, and we find a new definition of the classical affine W-superalgebra W(g,f,k)W(g,f,k) via the D-S reduction. This new construction allows us to find free generators of W(g,f,k)W(g,f,k), as a differential superalgebra, and two independent Lie brackets on W(g,f,k)/W(g,f,k).W(g,f,k)/\partial W(g,f,k). 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}
}