On cohomology theory for topological groups
Identifieur interne : 000576 ( Istex/Corpus ); précédent : 000575; suivant : 000577On cohomology theory for topological groups
Auteurs : Arati S. Khedekar ; C S RajanSource :
- Proceedings - Mathematical Sciences [ 0253-4142 ] ; 2012-05-01.
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Abstract
Abstract: We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of the identity. We show that if G and A are locally compact and second countable, then the second cohomology group based on locally continuous measurable cochains as above parametrizes the collection of locally split extensions of G by A.
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DOI: 10.1007/s12044-012-0067-6
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For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of the identity. We show that if <Emphasis Type="Italic">G</Emphasis> and <Emphasis Type="Italic">A</Emphasis> are locally compact and second countable, then the second cohomology group based on locally continuous measurable cochains as above parametrizes the collection of locally split extensions of <Emphasis Type="Italic">G</Emphasis> by <Emphasis Type="Italic">A</Emphasis>.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>Cohomology theory</Keyword><Keyword>group extension</Keyword><Keyword>locally compact groups</Keyword><Keyword>Lie groups</Keyword></KeywordGroup></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On cohomology theory for topological groups</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>On cohomology theory for topological groups</title></titleInfo><name type="personal" displayLabel="corresp"><namePart type="given">ARATI</namePart><namePart type="given">S</namePart><namePart type="family">KHEDEKAR</namePart><affiliation>School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Mumbai, India</affiliation><affiliation>E-mail: arati@math.tifr.res.in</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C</namePart><namePart type="given">S</namePart><namePart type="family">RAJAN</namePart><affiliation>School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Mumbai, India</affiliation><affiliation>E-mail: rajan@math.tifr.res.in</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">India</placeTerm></place><dateCreated encoding="w3cdtf">2011-01-06</dateCreated><dateIssued encoding="w3cdtf">2012-05-01</dateIssued><dateIssued encoding="w3cdtf">2012</dateIssued><copyrightDate encoding="w3cdtf">2012</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. 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