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arXiv · 1711.06344

Classical affine W-superalgebras via generalized Drinfeld-Sokolov reductions and related integrable systems

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

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BibTeXRIS

Uhi Rinn Suh. 2017-11-16. Classical affine W-superalgebras via generalized Drinfeld-Sokolov reductions and related integrable systems. https://doi.org/10.1007/s00220-017-3014-7

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