Generalized W-algebras and Integrable Hierarchies

TL;DR

This paper introduces generalized W-algebras derived from extended KdV hierarchies, revealing new classical W-algebras as their second Hamiltonian structures, including a construction of W_n^{(l)}.

Contribution

It presents a novel construction of generalized W-algebras from extended integrable hierarchies, expanding the understanding of classical W-algebras.

Findings

New classical W-algebras identified as Hamiltonian structures

Construction of W_n^{(l)} algebra provided

Extended KdV hierarchies linked to generalized W-algebras

Abstract

We report on generalizations of the KdV-type integrable hierarchies of Drinfel'd and Sokolov. These hierarchies lead to the existence of new classical $W$-algebras, which arise as the second Hamiltonian structure of the hierarchies. In particular, we present a construction of the $W_n^{(l)}$ algebras.