Rootsystems of simple Lie algebras
type: Item
instance of: scholarly article
title: Rootsystems of simple Lie algebras
zbMATH Open document ID: 0578.17011
DOI: 10.1016/0021-8693(85)90079-1
author: David J. Winter
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: This paper continues the investigation of the preceding article (cf. Zbl 0578.17010). -- It is shown that if \(L=\sum_{a\in R}L_ a\) is a simple nonclassical symmetric Lie algebra whose root system \(R\) contains no 2-section of type \(T_ 2\), then \(R\) is an irreducible Witt root system (i.e. with all nonzero roots Witt). Irreducible Witt root systems of prime rank (i.e. over \(\mathbb Z_ p)\) three are classified. Finally it is shown that the irreducible components of a Witt root system \(R\) are groups if and only if \(R\) excludes two specific types of irreducible Witt root systems of prime rank three. See also the following review Zbl 0578.17012.
Mathematics Subject Classification ID: 17B22
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 3925051
zbMATH Keywords: prime
zbMATH Keywords: characteristic
zbMATH Keywords: sections
zbMATH Keywords: symmetric Lie algebra
zbMATH Keywords: Witt root system
zbMATH Keywords: irreducible components
zbMATH Keywords: prime rank three
Wikidata QID: Q115366955
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90079-1
OpenAlex ID: W2077724477
cites work: Q5583129
cites work: Generalized classical Albert-Zassenhaus Lie algebras
cites work: Symmetric Lie algebras
description: scientific article; zbMATH DE number 3925051