Commutators in classical Lie algebras
type: Item
instance of: scholarly article
title: Commutators in classical Lie algebras
zbMATH Open document ID: 0714.17006
DOI: 10.1016/0024-3795(90)90258-E
author: Ralf Hirschbühl
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: The author shows that if a field K has enough elements or if its characteristic is suitably restricted, then for a given element A of a perfect classical Lie algebra \({\mathcal L}\) it is possible to compute in polynomial time X,Y\(\in {\mathcal L}\) such that \(A=[X,Y]\). For these algebras his results differ from those of the reviewer [Proc. Am. Math. Soc. 14, 763-767 (1963; Zbl 0135.073)] by giving, in most cases, a better lower bound for the number of elements in K, and employing a matrix-theoretical proof from which algorithms for the computation of X and Y can be derived.
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 4175200
zbMATH Keywords: additive commutator
zbMATH Keywords: lower bounds
zbMATH Keywords: number of elements in the field
zbMATH Keywords: special linear Lie algebras
zbMATH Keywords: odd orthogonal Lie algebras
zbMATH Keywords: even orthogonal Lie algebras
zbMATH Keywords: symplectic Lie algebras
zbMATH Keywords: algorithms
Wikidata QID: Q115364339
MaRDI profile type: Publication
cites work: Q5766912
cites work: Commutators of Matrices with Prescribed Determinant
cites work: Commutators in the Special and General Linear Groups
cites work: Commutators of matrices with coefficients from the field of two elements
cites work: On matrices of trace zero
cites work: On Commutators in a Simple Lie Algebra
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description: scientific article; zbMATH DE number 4175200