The Topography of $\W_\infty$-Type Algebras

TL;DR

This paper explores the structure of $ ext{W}_ ext{infty}$-type algebras by using a new one-parameter deformation, $ ext{W}_{k,p,q}$, connecting known algebras through various transformations.

Contribution

It introduces $ ext{W}_{k,p,q}$ as a unifying framework for $ ext{W}_ ext{infty}$-type algebras and relates existing algebras to this new deformation.

Findings

Unified description of $ ext{W}_ ext{infty}$-type algebras via $ ext{W}_{k,p,q}$

Connections established between known algebras and $ ext{W}_{k,p,q}$

Identification of special parameter values leading to known algebra reductions

Abstract

We chart out the landscape of $\Winfty$-type algebras using $\Wkpq$---a recently discovered one-parameter deformation of $\W_{\rm KP}$. We relate all hitherto known $\Winfty$-type algebras to $\Wkpq$ and its reductions, contractions, and/or truncations at special values of the parameter.