Supersymmetric Gelfand-Dickey Algebra

TL;DR

This paper explores the classical supersymmetric W-algebras, specifically W_2 and W_3, using the Gelfand-Dickey Hamiltonian framework to understand their algebraic structures.

Contribution

It provides a detailed analysis of supersymmetric W-algebras W_2 and W_3 via the Gelfand-Dickey Hamiltonian structure, advancing the understanding of their classical forms.

Findings

Explicit formulations of W_2 and W_3 supersymmetric algebras

Application of Gelfand-Dickey structure to supersymmetric cases

Enhanced understanding of classical supersymmetric W-algebras

Abstract

We study the classical version of supersymmetric $W$-algebras. Using the second Gelfand-Dickey Hamiltonian structure we work out in detail $W_2$ and $W_3$-algebras.