Simple Lie algebras of small characteristic. I: Sandwich elements
type: Item
instance of: scholarly article
title: Simple Lie algebras of small characteristic. I: Sandwich elements
zbMATH Open document ID: 0878.17019
author: Alexander Premet
author: Helmut Strade
published in: Journal of Algebra
publication date: 1997-06-24T00:00:00Z
review text: This paper is intended to contribute to the eventual classification of all simple Lie algebras of characteristics 5 and 7 by obtaining results analogous to a step in the already completed classification of such algebras for characteristic \(p > 7\). The authors investigate simple Lie algebras of absolute toral rank 2, an investigation in which sandwich elements have an important part. (An element \(c\) of a Lie algebra \(L\) is a sandwich of \(L\) if \((\text{ad} c)^2=0\).) The authors prove that if \(L\) is simple of absolute toral rank 2 over an algebraically closed field of characteristic \(p\geq 5\) and \(T\) is a 2-dimensional torus in the semisimple \(p\)-envelope of \(L\), then \(L\) is either classical or isomorphic to \(H(2;\mathbf{1};\Phi(\tau))^{(1)}\) or there is a 2-dimensional torus \(T'\) conjugate to \(T\) such that \(C_L(T')\) acts triangulably on \(L\) and \(L\) has homogeneous sandwiches with respect to \(T'\).
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 1013993
zbMATH Keywords: simple Lie algebras of characteristics 5 and 7
zbMATH Keywords: toral rank 2
zbMATH Keywords: sandwich elements
MaRDI profile type: Publication
full work available at URL: jabr.1996.6861
OpenAlex ID: W2065218045
Wikidata QID: Q115396050
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DOI: 10.1006/JABR.1996.6861
description: scientific article; zbMATH DE number 1013993