The classification of the simple modular Lie algebras. V: Algebras with Hamiltonian two-sections
type: Item
instance of: scholarly article
title: The classification of the simple modular Lie algebras. V: Algebras with Hamiltonian two-sections
zbMATH Open document ID: 0817.17022
DOI: 10.1007/BF02940784
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1995-08-08T00:00:00Z
review text: The classification of simple Lie algebras over algebraically closed fields of characteristic \(p>7\), whose completion was announced by the author and \textit{R. L. Wilson} [Bull. Am. Math. Soc., New Ser. 24, 357-362 (1991; Zbl 0725.17023)], was accomplished by dividing the investigation into cases defined by differing properties of one-sections and two- sections with respect to a torus of maximal absolute toral rank. This is the paper that considers the case in which there exists a nonclassical root and a two-section which has core \(H(2; 1;\Phi (\tau) )^{(1)}\). The conclusion that such an algebra is of Cartan type is achieved by showing the existence of a certain subalgebra satisfying the hypotheses of a recognition theorem of \textit{R. L. Wilson} [J. Algebra 40, 418-465 (1976; Zbl 0355.17012)].
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 706672
zbMATH Keywords: classification
zbMATH Keywords: simple modular Lie algebras
zbMATH Keywords: Hamiltonian two-sections
zbMATH Keywords: Cartan type
author: Helmut Strade
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 706672