A remark on Burnside's theorem on matrix algebras
type: Item
instance of: scholarly article
title: A remark on Burnside's theorem on matrix algebras
zbMATH Open document ID: 0554.15006
DOI: 10.1016/0024-3795(84)90141-1
author: Erik Rosenthal
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: Let L(V) be the algebra of linear operators on the finite dimensional vector space V over an algebraically closed field. Burnside's Theorem: If \({\mathcal A}\) is a transitive subalgebra of L(V) then \({\mathcal A}=L(V)\). A self-contained elementary proof is given. Although it is not explicitly stated, subalgebras are always assumed to contain the identity operator in this paper.
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 46H10
Mathematics Subject Classification ID: 47L30
zbMATH DE Number: 3882585
zbMATH Keywords: Burnside's theorem
zbMATH Keywords: operator algebras
zbMATH Keywords: graph transformations
zbMATH Keywords: transitive subalgebra
reviewed by: Thomas A. Farmer
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90141-1
OpenAlex ID: W2090712452
cites work: Q5550429
cites work: Q3293417
cites work: Burnside's Theorem on Algebras of Matrices
cites work: Q5822102
cites work: Q5686535
description: scientific article; zbMATH DE number 3882585