Classification of the Lie bialgebra structures on the Witt and Virasoro algebras
type: Item
instance of: scholarly article
title: Classification of the Lie bialgebra structures on the Witt and Virasoro algebras
zbMATH Open document ID: 0971.17008
DOI: 10.1016/S0022-4049(99)00045-6
author: Siu-Hung Ng
author: Earl J. Taft
published in: Journal of Pure and Applied Algebra
publication date: 2001-10-31T00:00:00Z
review text: Let \(k\) be a field of characteristic zero and let \(W\) be the Witt algebra over \(k\), which can be identified with the Lie algebra of derivations of the Laurent polynomial algebra \(k[t,t^{-1}]\). The one-sided Witt algebra \(W_1\) is the Lie algebra of derivations on the polynomial algebra \(k[t]\). The Virasoro algebra \(V\) is a certain central extension of \(W\). The authors prove that any Lie bialgebra structure on \(W_1\), \(W\) or \(V\) is a triangular coboundary Lie bialgebra structure associated to a skew-symmetric solution \(r\) of the classical Yang-Baxter equation of the form \(r=a\wedge b\).
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 17B68
zbMATH DE Number: 1501622
zbMATH Keywords: Lie bialgebra
zbMATH Keywords: Witt algebra
zbMATH Keywords: Virasoro algebra
zbMATH Keywords: classical Yang-Baxter equation
reviewed by: Sorin Dascalescu
MaRDI profile type: Publication
Wikidata QID: Q115340059
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full work available at URL: s0022-4049(99)00045-6
OpenAlex ID: W2024604757
description: scientific article; zbMATH DE number 1501622