Isotopy for Extended Affine Lie Algebras and Lie Tori
Identifieur interne : 000B83 ( Istex/Corpus ); précédent : 000B82; suivant : 000B84Isotopy for Extended Affine Lie Algebras and Lie Tori
Auteurs : Bruce Allison ; John FaulknerSource :
- Progress in Mathematics ; 2011.
Abstract
Summary: Centreless Lie tori have been used by E. Neher to construct all extended affine Lie algebras (EALAs). In this article, we study isotopy for centreless Lie tori, and show that Neher’s construction provides a 1–1 correspondence between centreless Lie tori up to isotopy and families of EALAs up to isomorphism. Also, centreless Lie tori can be coordinatized by unital algebras that are in general nonassociative, and, for many types of centreless Lie tori, there are classical definitions of isotopy for the coordinate algebras. We show for those types that an isotope of a Lie torus is coordinatized by an isotope of its coordinate algebra, thereby connecting the two notions of isotopy. In writing the article, we have not assumed prior knowledge of the theories of EALAs, Lie tori or isotopy.
Url:
DOI: 10.1007/978-0-8176-4741-4_1
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ISTEX:3963519ACC4BFF7B0CB93F7B09D314A218D52771Le document en format XML
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LLC</CopyrightHolderName><CopyrightYear>2011</CopyrightYear></ChapterCopyright><ChapterHistory><RegistrationDate><Year>2010</Year><Month>9</Month><Day>17</Day></RegistrationDate><OnlineDate><Year>2010</Year><Month>10</Month><Day>7</Day></OnlineDate></ChapterHistory><ChapterContext><SeriesID>4848</SeriesID><PartID>1</PartID><BookID>978-0-8176-4741-4</BookID><BookTitle>Developments and Trends in Infinite-Dimensional Lie Theory</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1_1" CorrespondingAffiliationID="Aff1_1"><AuthorName DisplayOrder="Western"><GivenName>Bruce</GivenName><FamilyName>Allison</FamilyName></AuthorName><Contact><Email>ballison@uvic.ca</Email></Contact></Author><Author AffiliationIDS="Aff2_1"><AuthorName DisplayOrder="Western"><GivenName>John</GivenName><FamilyName>Faulkner</FamilyName></AuthorName><Contact><Email>jrf@virginia.edu</Email></Contact></Author><Affiliation ID="Aff1_1"><OrgDivision>Department of Mathematics and Statistics</OrgDivision><OrgName>University of Victoria</OrgName><OrgAddress><City>Victoria</City><State>BC</State><Postcode>V8W 3P4</Postcode><Country>Canada</Country></OrgAddress></Affiliation><Affiliation ID="Aff2_1"><OrgDivision>Department of Mathematics</OrgDivision><OrgName>University of Virginia</OrgName><OrgAddress><City>Charlottesville</City><State>VA</State><Postcode>22904-4137</Postcode><Country>USA</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1_1" Language="En" OutputMedium="All"><Heading>Summary</Heading><Para>Centreless Lie tori have been used by E. Neher to construct all extended affine Lie algebras (EALAs). In this article, we study isotopy for centreless Lie tori, and show that Neher’s construction provides a 1–1 correspondence between centreless Lie tori up to isotopy and families of EALAs up to isomorphism. Also, centreless Lie tori can be coordinatized by unital algebras that are in general nonassociative, and, for many types of centreless Lie tori, there are classical definitions of isotopy for the coordinate algebras. We show for those types that an isotope of a Lie torus is coordinatized by an isotope of its coordinate algebra, thereby connecting the two notions of isotopy. In writing the article, we have not assumed prior knowledge of the theories of EALAs, Lie tori or isotopy.</Para></Abstract><KeywordGroup Language="En" OutputMedium="All"><Heading>Key words</Heading><Keyword>isotope</Keyword><Keyword>extended affine Lie algebra</Keyword><Keyword>Lie torus</Keyword><Keyword>nonassociative algebra</Keyword><Keyword>Jordan algebra</Keyword><Keyword>alternative algebra</Keyword></KeywordGroup><ArticleNote Type="Misc"><SimplePara><Emphasis Type="Italic">2000 Mathematics Subject Classifications:</Emphasis> Primary 17B65, 17A01. Secondary 17B60,17B70, 17C99, 17D05.</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Isotopy for Extended Affine Lie Algebras and Lie Tori</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Isotopy for Extended Affine Lie Algebras and Lie Tori</title></titleInfo><name type="personal" displayLabel="corresp"><namePart type="given">Bruce</namePart><namePart type="family">Allison</namePart><affiliation>Department of Mathematics and Statistics, University of Victoria, V8W 3P4, Victoria, BC, Canada</affiliation><affiliation>E-mail: ballison@uvic.ca</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">John</namePart><namePart type="family">Faulkner</namePart><affiliation>Department of Mathematics, University of Virginia, 22904-4137, Charlottesville, VA, USA</affiliation><affiliation>E-mail: jrf@virginia.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="research-article" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Birkhäuser Boston</publisher><place><placeTerm type="text">Boston</placeTerm></place><dateIssued encoding="w3cdtf">2010-10-07</dateIssued><copyrightDate encoding="w3cdtf">2011</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Summary: Centreless Lie tori have been used by E. Neher to construct all extended affine Lie algebras (EALAs). In this article, we study isotopy for centreless Lie tori, and show that Neher’s construction provides a 1–1 correspondence between centreless Lie tori up to isotopy and families of EALAs up to isomorphism. Also, centreless Lie tori can be coordinatized by unital algebras that are in general nonassociative, and, for many types of centreless Lie tori, there are classical definitions of isotopy for the coordinate algebras. We show for those types that an isotope of a Lie torus is coordinatized by an isotope of its coordinate algebra, thereby connecting the two notions of isotopy. In writing the article, we have not assumed prior knowledge of the theories of EALAs, Lie tori or isotopy.</abstract><relatedItem type="host"><titleInfo><title>Developments and Trends in Infinite-Dimensional Lie Theory</title></titleInfo><name type="personal"><namePart type="given">Karl-Hermann</namePart><namePart type="family">Neeb</namePart><affiliation>Friedrich-Alexander-Universität Erlangen, Department of Mathematics, Bismarckstrasse 1 1/2, 91054, Erlangen, Germany</affiliation><affiliation>E-mail: neeb@mi.uni-erlangen.de</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Arturo</namePart><namePart type="family">Pianzola</namePart><affiliation>University of Alberta, Department of Mathematical Sciences, T6G 2G1, Edmonton, Alberta, Canada</affiliation><affiliation>E-mail: a.pianzola@gmail.com</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Contributed volume" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2011</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11649">Mathematics and Statistics</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="SCM">Mathematics</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM11132">Topological Groups, Lie Groups</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM11078">Group Theory and Generalizations</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM11000">Algebra</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM21006">Geometry</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM11019">Algebraic Geometry</topic></subject><identifier type="DOI">10.1007/978-0-8176-4741-4</identifier><identifier type="ISBN">978-0-8176-4740-7</identifier><identifier type="eISBN">978-0-8176-4741-4</identifier><identifier type="BookTitleID">152257</identifier><identifier type="BookID">978-0-8176-4741-4</identifier><identifier type="BookChapterCount">14</identifier><identifier type="BookVolumeNumber">288</identifier><identifier type="BookSequenceNumber">288</identifier><identifier type="PartChapterCount">6</identifier><part><date>2011</date><detail type="part"><title>Infinite-Dimensional Lie (Super-)Algebras</title></detail><detail type="volume"><number>288</number><caption>vol.</caption></detail><extent unit="pages"><start>3</start><end>43</end></extent></part><recordInfo><recordOrigin>Springer Science+Business Media, LLC, 2011</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Progress in Mathematics</title></titleInfo><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2011</copyrightDate><issuance>serial</issuance></originInfo><identifier type="SeriesID">4848</identifier><recordInfo><recordOrigin>Springer Science+Business Media, LLC, 2011</recordOrigin></recordInfo></relatedItem><identifier type="istex">3963519ACC4BFF7B0CB93F7B09D314A218D52771</identifier><identifier type="ark">ark:/67375/HCB-95BVTX9W-6</identifier><identifier type="DOI">10.1007/978-0-8176-4741-4_1</identifier><identifier type="ChapterID">1</identifier><identifier type="ChapterID">b978-0-8176-4741-4_1</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer Science+Business Media, LLC, 2011</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>Springer Science+Business Media, LLC, 2011</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/3963519ACC4BFF7B0CB93F7B09D314A218D52771/metadata/json</uri></json:item></metadata><annexes><json:item><extension>txt</extension><original>true</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/3963519ACC4BFF7B0CB93F7B09D314A218D52771/annexes/txt</uri></json:item></annexes></istex></record>Pour manipuler ce document sous Unix (Dilib)
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