A characterization of certain loop Lie algebras
type: Item
instance of: scholarly article
title: A characterization of certain loop Lie algebras
zbMATH Open document ID: 0946.17013
author: J. Marshall Osborn
author: Kaiming Zhao
published in: Journal of Algebra
publication date: 2000-10-19T00:00:00Z
review text: The authors classify \({\mathbb Z} \times {\mathbb Z}\)-graded Lie algebras \(A = \bigoplus_{i,j\in {\mathbb Z}} A_{ij}\) over a field of characteristic zero with \(\dim A_{i,j} \leqq 1\) such that \(A_{\pm 1,0}\) and \(A_{0,\pm 1}\) are one-dimensional and generate \(A_1 \bigoplus_{i\in {\mathbb Z}} A_{0,j} \cong s\ell_2\), \([A_{-1,0} ,A_{1,0} ] = 0\), and \(\operatorname {ad} A_{\pm 1,0}\) act faithfully on \(\bigoplus_{i\in {\mathbb Z}} A_{j,1}\). They show that \(A\) must be isomorphic to one of the two smaller loop algebras.
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B65
zbMATH DE Number: 1384450
zbMATH Keywords: graded Lie algebras
zbMATH Keywords: loop algebras
Wikidata QID: Q115395800
MaRDI profile type: Publication
full work available at URL: jabr.1999.7994
OpenAlex ID: W2062719628
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cites work: Q3704051
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DOI: 10.1006/JABR.1999.7994
description: scientific article; zbMATH DE number 1384450