Nilpotent locally convex Lie algebras and Lie field structures
Identifieur interne : 000370 ( Istex/Corpus ); précédent : 000369; suivant : 000371Nilpotent locally convex Lie algebras and Lie field structures
Auteurs : N. LimiSource :
- Communications in Mathematical Physics [ 0010-3616 ] ; 1969-06-01.
English descriptors
- KwdEn :
- Algebra, Bilinear mapping, Central element, Characteristic function, Commutative subalgebra, Compact groups, Complete normed, Complex numbers, Composition rule, Continuous functions, Continuous representations, Convex, Convex kernel, Field structures, Finite number, Group operation, Hilbert, Hilbert space, Hilbert spaces, Hitbert space, Inhomogeneous lorentz group, Invariant functionals, Kernel topology, Linear mapping, Linear space, Linear subspace, Mapping, Metrizable space, Natural number, Neighbourhood, Nilpotent normed, Normed, Other topology, Periodic function, Periodic functions, Quantum field theory, Quasinilpotent, Quasinilpotent operator, Real numbers, Right translations, Same time, Separable hilbert space, Simultaneous continuity, Strict inductive limes, Subalgebra, Subgroup, Subnormalizer, Theoretical physics, Topological, Topological group, Topological groups, Topology, Unitary representations, Vector space.
- Teeft :
- Algebra, Bilinear mapping, Central element, Characteristic function, Commutative subalgebra, Compact groups, Complete normed, Complex numbers, Composition rule, Continuous functions, Continuous representations, Convex, Convex kernel, Field structures, Finite number, Group operation, Hilbert, Hilbert space, Hilbert spaces, Hitbert space, Inhomogeneous lorentz group, Invariant functionals, Kernel topology, Linear mapping, Linear space, Linear subspace, Mapping, Metrizable space, Natural number, Neighbourhood, Nilpotent normed, Normed, Other topology, Periodic function, Periodic functions, Quantum field theory, Quasinilpotent, Quasinilpotent operator, Real numbers, Right translations, Same time, Separable hilbert space, Simultaneous continuity, Strict inductive limes, Subalgebra, Subgroup, Subnormalizer, Theoretical physics, Topological, Topological group, Topological groups, Topology, Unitary representations, Vector space.
Abstract
Abstract: The purpose of this work is to join Lie field structures with certain infinite-dimensional Lie algebras with locally convex topology. These topological Lie algebras allow topological groups which are a generalization of the connected nilpotent Lie groups. We showed the existence of the continuous unitary representations of the gained groups and then we proved the analogue of Gårding theorem. Using this theorem we established the existence of representations of Lie field structures into Lie algebras of skew-symmetric operators on Hilbert spaces.
Url:
DOI: 10.1007/BF01645132
Links to Exploration step
ISTEX:118DB5C81A51A66CBB9B96D6F468C3C5C5EF3839Le document en format XML
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Phys.</title><idno type="pISSN">0010-3616</idno><idno type="eISSN">1432-0916</idno><idno type="journal-ID">true</idno><idno type="issue-article-count">5</idno><idno type="volume-issue-count">4</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="1969-06-01"></date><biblScope unit="volume">14</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="89">89</biblScope><biblScope unit="page" to="107">107</biblScope></imprint></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1969-03-08</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: The purpose of this work is to join Lie field structures with certain infinite-dimensional Lie algebras with locally convex topology. These topological Lie algebras allow topological groups which are a generalization of the connected nilpotent Lie groups. We showed the existence of the continuous unitary representations of the gained groups and then we proved the analogue of Gårding theorem. Using this theorem we established the existence of representations of Lie field structures into Lie algebras of skew-symmetric operators on Hilbert spaces.</p></abstract><textClass><keywords scheme="Journal Subject"><list><head>Physics</head><item><term>Quantum Physics</term></item><item><term>Mathematical and Computational Physics</term></item><item><term>Quantum Computing, Information and Physics</term></item><item><term>Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks</term></item><item><term>Statistical Physics</term></item><item><term>Relativity and Cosmology</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1969-03-08">Created</change><change when="1969-06-01">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-11-30">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/118DB5C81A51A66CBB9B96D6F468C3C5C5EF3839/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus springer-journals not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType><istex:document><Publisher><PublisherInfo><PublisherName>Springer-Verlag</PublisherName><PublisherLocation>Berlin/Heidelberg</PublisherLocation></PublisherInfo><Journal><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>220</JournalID><JournalPrintISSN>0010-3616</JournalPrintISSN><JournalElectronicISSN>1432-0916</JournalElectronicISSN><JournalTitle>Communications in Mathematical Physics</JournalTitle><JournalAbbreviatedTitle>Commun.Math. 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These topological Lie algebras allow topological groups which are a generalization of the connected nilpotent Lie groups. We showed the existence of the continuous unitary representations of the gained groups and then we proved the analogue of Gårding theorem. Using this theorem we established the existence of representations of Lie field structures into Lie algebras of skew-symmetric operators on Hilbert spaces.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>Work supported by National Science Foundation.</SimplePara></ArticleNote><ArticleNote Type="Misc"><SimplePara>On leave of absence from the Institute “Rudjer Bošković”, Zagreb.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Nilpotent locally convex Lie algebras and Lie field structures</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Nilpotent locally convex Lie algebras and Lie field structures</title></titleInfo><name type="personal"><namePart type="given">N.</namePart><namePart type="family">Limić</namePart><affiliation>Institute for Advanced Study, Princeton, New Jersey</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">Berlin/Heidelberg</placeTerm></place><dateCreated encoding="w3cdtf">1969-03-08</dateCreated><dateIssued encoding="w3cdtf">1969-06-01</dateIssued><dateIssued encoding="w3cdtf">1969</dateIssued><copyrightDate encoding="w3cdtf">1969</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: The purpose of this work is to join Lie field structures with certain infinite-dimensional Lie algebras with locally convex topology. These topological Lie algebras allow topological groups which are a generalization of the connected nilpotent Lie groups. We showed the existence of the continuous unitary representations of the gained groups and then we proved the analogue of Gårding theorem. Using this theorem we established the existence of representations of Lie field structures into Lie algebras of skew-symmetric operators on Hilbert spaces.</abstract><relatedItem type="host"><titleInfo><title>Communications in Mathematical Physics</title></titleInfo><titleInfo type="abbreviated"><title>Commun.Math. 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