Derivations of the Lie algebra of strictly upper triangular matrices over a commutative ring
type: Item
instance of: scholarly article
title: Derivations of the Lie algebra of strictly upper triangular matrices over a commutative ring
zbMATH Open document ID: 1135.17010
author: Shikun Ou
author: Dengyin Wang
author: Ruiping Yao
published in: Linear Algebra and its Applications
publication date: 2007-06-26T00:00:00Z
review text: For an arbitrary commutative ring with identity \(R\), all \(n\times n\) matrices over \(R\), denoted by \(\text{gl}(n,R)\), is a Lie algebra under the usual operations of matrices and it is called the general linear Lie algebra. Let \(N(n, R)\) denotes the subalgebra consisting of all strictly upper triangular matrices, the authors of the paper describe an explicit form of all the derivations of it.
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 17B45
Mathematics Subject Classification ID: 13C10
zbMATH DE Number: 5167482
zbMATH Keywords: commutative rings
zbMATH Keywords: linear Lie algebras
zbMATH Keywords: derivations of Lie algebras
Wikidata QID: Q115344904
reviewed by: Xiandong Wang
MaRDI profile type: Publication
full work available at URL: j.laa.2007.02.003
OpenAlex ID: W2015385053
cites work: A note on algebra automorphisms of strictly upper triangular matrices over commutative rings
cites work: Automorphisms of the Lie algebra of upper triangular matrices over a connected commutative ring
cites work: Automorphisms of certain Lie algebras of upper triangular matrices over a commutative ring
cites work: Automorphisms of the Lie algebra of strictly upper triangular matrices over certain commutative rings
cites work: Automorphisms of the Lie algebra of strictly upper triangular matrices over a commutative ring
cites work: Derivations of the parabolic subalgebras of the general linear Lie algebra over a commutative ring
cites work: Derivations of the intermediate Lie algebras between the Lie algebra of diagonal matrices and that of upper triangular matrices over a commutative ring
DOI: 10.1016/J.LAA.2007.02.003
description: scientific article; zbMATH DE number 5167482