What is a lattice W-algebra?

TL;DR

This paper introduces lattice analogs of classical W_m-algebras using Poisson-Lie groups of pseudo-difference operators and demonstrates their equivalence to algebras obtained via discrete Drinfeld-Sokolov reduction.

Contribution

It defines lattice W-algebras through Poisson-Lie groups and proves their equivalence to those from discrete Drinfeld-Sokolov reduction, linking continuous and discrete algebraic structures.

Findings

Lattice W-algebras are constructed using Poisson-Lie groups of pseudo-difference operators.

The constructed lattice W-algebras coincide with those from discrete Drinfeld-Sokolov reduction.

The work bridges continuous and discrete algebraic frameworks for W-algebras.

Abstract

We employ the Poisson-Lie group of pseudo-difference operators to define lattice analogs of classical $W_m$-algebras. We then show that the so-constructed algebras coincide with the ones given by discrete Drinfeld-Sokolov type reduction.