Trace-positive polynomials and the quartic tracial moment problem

Lade...
Vorschaubild
Dateien
269.pdf
269.pdfGröße: 355.7 KBDownloads: 279
Datum
2010
Herausgeber:innen
Kontakt
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
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
Working Paper/Technical Report
Publikationsstatus
Published
Erschienen in
Zusammenfassung

The tracial analog of Hilbert's classical result on positive binary quartics is presented: a trace-positive bivariate noncommutative polynomial of degree at most four is a sum of hermitian squares and commutators.
This is applied via duality to investigate the truncated tracial moment problem: a sequence of real numbers indexed by words of degree four in two noncommuting variables with values invariant under cyclic permutations of the indexes, can be represented with tracial moments of matrices if the corresponding moment matrix is positive definite. Understanding trace-positive polynomials and the tracial moment problem is one of the approaches to Connes' embedding conjecture.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
nichtkommutative Polynome, Spur, Summen hermitescher Quadrate, noncommutative polynomials, trace, sums of hermitian squares, moment problem
Konferenz
Rezension
undefined / . - undefined, undefined
Forschungsvorhaben
Organisationseinheiten
Zeitschriftenheft
Datensätze
Zitieren
ISO 690BURGDORF, Sabine, Igor KLEP, 2010. Trace-positive polynomials and the quartic tracial moment problem
BibTex
@techreport{Burgdorf2010Trace-655,
  year={2010},
  series={Konstanzer Schriften in Mathematik},
  title={Trace-positive polynomials and the quartic tracial moment problem},
  number={269},
  author={Burgdorf, Sabine and Klep, Igor}
}
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/123456789/655">
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/655/1/269.pdf"/>
    <dc:creator>Burgdorf, Sabine</dc:creator>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/655"/>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/655/1/269.pdf"/>
    <dcterms:abstract xml:lang="eng">The tracial analog of Hilbert's classical result on positive binary quartics is presented: a trace-positive bivariate noncommutative polynomial of degree at most four is a sum of hermitian squares and commutators.&lt;br /&gt;This is applied via duality to investigate the truncated tracial moment problem: a sequence of real numbers indexed by words of degree four in two noncommuting variables with values invariant under cyclic permutations of the indexes, can be represented with tracial moments of matrices if the corresponding moment matrix is positive definite. Understanding trace-positive polynomials and the tracial moment problem is one of the approaches to Connes' embedding conjecture.</dcterms:abstract>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dcterms:title>Trace-positive polynomials and the quartic tracial moment problem</dcterms:title>
    <dc:format>application/pdf</dc:format>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:issued>2010</dcterms:issued>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Burgdorf, Sabine</dc:contributor>
    <dc:language>eng</dc:language>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/52"/>
    <dc:creator>Klep, Igor</dc:creator>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/52"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:45:24Z</dcterms:available>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:45:24Z</dc:date>
    <dc:contributor>Klep, Igor</dc:contributor>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:rights>terms-of-use</dc:rights>
  </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
Ja
Begutachtet
Diese Publikation teilen