On the generators of Lie superalgebras
type: Item
instance of: scholarly article
title: On the generators of Lie superalgebras
zbMATH Open document ID: 0768.17001
DOI: 10.1016/0024-3795(93)90022-G
author: Helena Albuquerque
author: Alberto Elduque
published in: Linear Algebra and its Applications
publication date: 1993-05-16T00:00:00Z
review text: Any finite-dimensional semisimple Lie algebra \(G\) over a field of characteristic zero is generated by two elements --- this result was first proved in 1949, but appears to be not commonly known [see \textit{T. Ionescu}, Linear Algebra Appl. 15, 271--292 (1976; Zbl 0358.17014), or the first author and \textit{F. Silva Leite}, ibid. 119, 51--56 (1989; Zbl 0676.17006)]. In the present paper, the methods of Ionescu are used to show that any classical simple Lie superalgebra (with nontrivial odd part) over an algebraically closed field of characteristic zero can be generated by only one single element.
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 167832
zbMATH Keywords: generators
zbMATH Keywords: simple Lie superalgebra
MaRDI profile type: Publication
Wikidata QID: Q115364322
cites work: On the generators of semisimple Lie algebras
cites work: Q3882586
cites work: Lie superalgebras
cites work: Q4283795
cites work: The theory of Lie superalgebras. An introduction
description: scientific article; zbMATH DE number 167832