Automorphisms of a linear Lie algebra over a commutative ring
type: Item
instance of: scholarly article
title: Automorphisms of a linear Lie algebra over a commutative ring
zbMATH Open document ID: 1124.17007
author: Dengyin Wang
author: Qiu Yu
author: Yanxia Zhao
published in: Linear Algebra and its Applications
publication date: 2007-05-10T00:00:00Z
review text: Let \(R\) be a commutative ring with identity. \textit{Y. Cao} showed [J. Algebra 189, No. 2, 506--513 (1997; Zbl 0878.17016)] that each automorphism of \(t\), the Lie algebra of upper triangular matrices over \(R\), is the product of three types of automorphisms: central, graph and inner. In this paper the author shows a similar result for the standard Borel subalgebra of the orthogonal Lie algebra \(o(2m,R)\), where \(m\) is greater than 4 and 2 is invertible in \(R\). It is necessary to find automorphisms to take the place of those in Cao's result.
reviewed by: Ernest L. Stitzinger
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 5151570
zbMATH Keywords: Orthogonal Lie algebra
zbMATH Keywords: automorphism
Wikidata QID: Q115344907
MaRDI profile type: Publication
full work available at URL: j.laa.2007.01.003
OpenAlex ID: W1992659431
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 a commutative ring
cites work: A note on algebra automorphisms of strictly upper triangular matrices over commutative rings
cites work: Automorphisms and derivations of upper triangular matrix rings
cites work: Jordan isomorphisms of triangular matrix algebras over a connected commutative ring
cites work: Decomposition of Jordan automorphisms of strictly triangular matrix algebra over local rings
DOI: 10.1016/J.LAA.2007.01.003
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description: scientific article; zbMATH DE number 5151570