Algèbres simples centrales à involution de première espèce

Lade...
Vorschaubild
Dateien
becher6.pdf
becher6.pdfGröße: 168.14 KBDownloads: 308
Datum
2004
Herausgeber:innen
Kontakt
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
DOI (zitierfähiger Link)
ArXiv-ID
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Open Access Green
Core Facility der Universität Konstanz
Gesperrt bis
Titel in einer weiteren Sprache
Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published
Erschienen in
Bulletin of the Belgian Mathematical Society - Simon Stevin. 2004, 11(4), pp. 603-615
Zusammenfassung

This article provides new and elementary proofs for some of the crucial theorems in the theory of central simple algebras with involution of the first kind. In the first place Albert's criterion for the existence of an involution of the first kind and Kneser's extension theorem for such involutions are presented in a unified way. These two results are retrieved as corollaries of a new theorem which gives a criterion to decide whether an antiautomorphism of a central simple algebra is an involution of the first kind. Two examples are given to indicate that the analogous approach cannot be applied to involutions of the second kind. Quaternion algebras give the easiest nontrivial examples of central simple algebras which carry an involution of the first kind. Albert has shown that any central simple algebra of dimension $16$ with involution of the first kind is a tensor product of two quaternion algebras. This theorem is presented here with a new proof essentially using basic linear algebra.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
central simple algebra, involution of first kind, antiautomorphism, biquaternion algebra
Konferenz
Rezension
undefined / . - undefined, undefined
Forschungsvorhaben
Organisationseinheiten
Zeitschriftenheft
Datensätze
Zitieren
ISO 690BECHER, Karim Johannes, 2004. Algèbres simples centrales à involution de première espèce. In: Bulletin of the Belgian Mathematical Society - Simon Stevin. 2004, 11(4), pp. 603-615
BibTex
@article{Becher2004Algeb-604,
  year={2004},
  title={Algèbres simples centrales à involution de première espèce},
  number={4},
  volume={11},
  journal={Bulletin of the Belgian Mathematical Society - Simon Stevin},
  pages={603--615},
  author={Becher, Karim Johannes}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/604">
    <dcterms:abstract xml:lang="eng">This article provides new and elementary proofs for some of the crucial theorems in the theory of central simple algebras with involution of the first kind. In the first place Albert's criterion for the existence of an involution of the first kind and Kneser's extension theorem for such involutions are presented in a unified way. These two results are retrieved as corollaries of a new theorem which gives a criterion to decide whether an antiautomorphism of a central simple algebra is an involution of the first kind. Two examples are given to indicate that the analogous approach cannot be applied to involutions of the second kind. Quaternion algebras give the easiest nontrivial examples of central simple algebras which carry an involution of the first kind. Albert has shown that any central simple algebra of dimension $16$ with involution of the first kind is a tensor product of two quaternion algebras. This theorem is presented here with a new proof essentially using basic linear algebra.</dcterms:abstract>
    <dc:format>application/pdf</dc:format>
    <dcterms:issued>2004</dcterms:issued>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:45:12Z</dc:date>
    <dc:language>eng</dc:language>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:45:12Z</dcterms:available>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/604/1/becher6.pdf"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/604/1/becher6.pdf"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/52"/>
    <dcterms:title>Algèbres simples centrales à involution de première espèce</dcterms:title>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>Becher, Karim Johannes</dc:creator>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dcterms:bibliographicCitation>First publ. in: Bulletin of the Belgian Mathematical Society - Simon Stevin 11 (2004), 4, pp. 603-615</dcterms:bibliographicCitation>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/52"/>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/604"/>
    <dc:rights>terms-of-use</dc:rights>
    <dc:contributor>Becher, Karim Johannes</dc:contributor>
  </rdf:Description>
</rdf:RDF>
Interner Vermerk
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Kontakt
URL der Originalveröffentl.
Prüfdatum der URL
Prüfungsdatum der Dissertation
Finanzierungsart
Kommentar zur Publikation
Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Nein
Begutachtet
Diese Publikation teilen