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The Wielandt Subalgebra of a Lie Algebra

Barnes, Donald W; Groves, Daniel

Description

Following the analogy with group theory, we define the Wielandt subalgebra of a finite-dimensional Lie algebra to be the intersection of the normalisers of the subnormal subalgebras. In a non-zero algebra,this is a non-zero ideal if the ground field has characteristic 0 or if the derived algebra is nilpotent, allowing the definition of the Wielandt series. For a Lie algebra with nilpotent derived algebra, we obtain a bound for the derived length in terms of the Wielandt length and show this...[Show more]

dc.contributor.authorBarnes, Donald W
dc.contributor.authorGroves, Daniel
dc.date.accessioned2015-12-13T22:27:56Z
dc.date.available2015-12-13T22:27:56Z
dc.identifier.issn1446-7887
dc.identifier.urihttp://hdl.handle.net/1885/74179
dc.description.abstractFollowing the analogy with group theory, we define the Wielandt subalgebra of a finite-dimensional Lie algebra to be the intersection of the normalisers of the subnormal subalgebras. In a non-zero algebra,this is a non-zero ideal if the ground field has characteristic 0 or if the derived algebra is nilpotent, allowing the definition of the Wielandt series. For a Lie algebra with nilpotent derived algebra, we obtain a bound for the derived length in terms of the Wielandt length and show this bound to be best possible. We also characterise the Lie algebras with nilpotent derived algebra and Wielandt length 2.
dc.publisherAustralian Mathematics Publishing Association
dc.sourceJournal of the Australian Mathematical Society
dc.subjectKeywords: Lie algebras; Subnormal subalgebras
dc.titleThe Wielandt Subalgebra of a Lie Algebra
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume74
dc.date.issued2003
local.identifier.absfor010105 - Group Theory and Generalisations
local.identifier.ariespublicationMigratedxPub3999
local.type.statusPublished Version
local.contributor.affiliationBarnes, Donald W, no formal affiliation
local.contributor.affiliationGroves, Daniel, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.startpage313
local.bibliographicCitation.lastpage330
dc.date.updated2015-12-11T08:35:58Z
local.identifier.scopusID2-s2.0-30244575547
CollectionsANU Research Publications

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