Integrable structure of the classical lattice \(W_n\) algebra
type: Item
instance of: scholarly article
title: Integrable structure of the classical lattice \(W_n\) algebra
zbMATH Open document ID: 0966.37036
DOI: 10.1016/S0960-0779(97)00142-2
author: Kazuhiro Hikami
published in: Chaos, Solitons and Fractals
publication date: 2001-08-21T00:00:00Z
review text: The integrable structure of the lattice analogue of the \(W_N\) algebra is considered. The author reviews the lattice Virasoro algebra. The elementary dynamical variable is introduced and a generalization to the lattice \(W_N\) algebra is considered. The author constructs the \(N\times N\) Lax matrix in terms of the elementary dynamical variables, and shows that the monodromy matrix has a fundamental Poisson structure with the \(\mathbb{Z}_N\) invariant classical \(r\)-matrix.
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 37K60
Mathematics Subject Classification ID: 37L60
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1370464
zbMATH Keywords: integrable structure
zbMATH Keywords: lattice Virasoro algebra
zbMATH Keywords: Lax matrix
MaRDI profile type: Publication
cites work: Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
cites work: Q4003380
cites work: POISSON–LIE GROUPS AND CLASSICAL W-ALGEBRAS
description: scientific article; zbMATH DE number 1370464