Lattice analogues of W-algebras and Classical Integrable Equations

TL;DR

This paper introduces a systematic method to construct lattice versions of W-algebras, derives a lattice Boussinesq equation, and explores connections with q-deformed Virasoro algebra, advancing the understanding of integrable systems.

Contribution

It provides explicit lattice constructions of W-algebras and derives a lattice Boussinesq equation from Hamiltonian dynamics, linking classical and quantum algebraic structures.

Findings

Explicit lattice W-algebras constructed for classical and quantum cases.

Derived lattice Boussinesq equation from Hamiltonian equations.

Discussed connection between lattice Faddeev-Takhtadjan-Volkov algebra and q-deformed Virasoro.

Abstract

We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian equations of motion. Connection between the lattice Faddeev-Takhtadjan-Volkov algebra [1] and q-deformed Virasoro is also discussed.