Rank one Lie algebras
type: Item
instance of: scholarly article
title: Rank one Lie algebras
zbMATH Open document ID: 0563.17011
DOI: 10.2307/2007082
author: Georgia Benkart
author: J. Marshall Osborn
published in: Annals of Mathematics. Second Series
publication date: 1984-01-01T00:00:00Z
review text: The main theorem of the paper under review has been announced [Contemp. Math. 13, 263-265 (1982; Zbl 0504.17003)]: Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of prime characteristic \(p>7\). If L has a one-dimensional Cartan subalgebra, then L is isomorphic to the three-dimensional algebra \({\mathfrak sl}(2)\) or to an Albert-Zassenhaus Lie algebra. As the authors mention, the result is true for characteristics 5 and 7 as well. The proof including the cases \(p=5\) and \(p=7\) is based on more technical calculations and is not given in the paper.
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 3897173
zbMATH Keywords: modular Lie algebras
zbMATH Keywords: simple Lie algebra
zbMATH Keywords: prime characteristic
zbMATH Keywords: one- dimensional Cartan subalgebra
zbMATH Keywords: Albert-Zassenhaus Lie algebra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2007082
OpenAlex ID: W2321135829
description: scientific article; zbMATH DE number 3897173