Toral rank one simple Lie algebras of low characteristics
type: Item
instance of: scholarly article
title: Toral rank one simple Lie algebras of low characteristics
zbMATH Open document ID: 0894.17018
author: Serge Skryabin
published in: Journal of Algebra
publication date: 1998-04-13T00:00:00Z
review text: The author classifies the toral rank one simple Lie algebras over algebraically closed fields of characteristic \(p=2,3\). This corresponds to one of the basic steps in the successful classification of the simple finite-dimensional Lie algebras over algebraically closed fields of characteristic \(p>7\). His result is that \(sl(2)\) and \(psl(3)\) are the only such algebras for \(p=3\), and no such algebras exist for \(p=2\). The techniques required for this classification in small characteristics differ significantly from those that have been used in the case \(p>7\). In the process of this study the author has also obtained results on such topics as simple Lie algebras \(L\) containing a Cartan subalgebra of toral rank 1 in \(L\) and the structure of certain exceptional Hamiltonian algebras of characteristic 3.
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 1139794
zbMATH Keywords: toral rank one simple Lie algebras
zbMATH Keywords: Cartan subalgebra of toral rank 1
zbMATH Keywords: exceptional Hamiltonian algebras of characteristic 3
MaRDI profile type: Publication
Wikidata QID: Q115395930
full work available at URL: jabr.1997.7231
OpenAlex ID: W2001896067
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DOI: 10.1006/JABR.1997.7231
description: scientific article; zbMATH DE number 1139794