On linear subspaces of nilpotent elements in a Lie algebra
type: Item
instance of: scholarly article
title: On linear subspaces of nilpotent elements in a Lie algebra
zbMATH Open document ID: 0941.17004
DOI: 10.1016/S0024-3795(98)10010-1
author: Roy Meshulam
author: Nizar Radwan
published in: Linear Algebra and its Applications
publication date: 1999-12-06T00:00:00Z
review text: Let \(L\) be a complex semisimple Lie algebra. The authors show that if \(W\) is a linear subspace of ad-nilpotent elements, then \(\dim W\leq \frac 12(\dim L-\operatorname {rank }L)\). They also prove that the maximal dimension of a linear space of symmetric nilpotent \(n\times n\) complex matrices is \(\frac 14 n^2\).
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 1355349
zbMATH Keywords: nilpotent matrices
zbMATH Keywords: spaces of matrices
zbMATH Keywords: semisimple Lie algebra
Wikidata QID: Q115339988
reviewed by: Melih Boral
MaRDI profile type: Publication
cites work: On Nilalgebras and Linear Varieties of Nilpotent Matrices, I
cites work: Linear spaces of Toeplitz and nilpotent matrices
cites work: Linear spaces of nilpotent matrices
cites work: Q4527707
description: scientific article; zbMATH DE number 1355349