<div class="csl-bib-body">
<div class="csl-entry">Wödlinger, M. G. (2018). <i>Highest weight representations of the virasoro algebra</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2018.59983</div>
</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2018.59983
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/7925
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dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
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dc.description.abstract
The Virasoro algebra plays a fundamental role in modern research areas such as condensed matter physics or quantum gravity. Applying the theory requires a deep understanding of the underlying mathematical structure. Here, we define the Virasoro algebra as the unique central extension to the Witt algebra. The investigation of the Virasoro algebra leads to Verma modules and the Hermitian Shapovalov form which is used to define unitary highest weight representations. Subsequently, we investigate the Hermitian form and compute an explicit expression for the Kac-determinant. We use the determinant formula to obtain first results about the classification of unitary highest weight representations. To complete the classification, we explicitly construct unitary highest weight representations of the Virasoro algebra from factor algebras of affine Lie algebras. We conclude the investigation with some calculations regarding the Ising model and a short introduction to the applications of the Virasoro algebra in condensed matter physics and gravity.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Darstellungstheorie
de
dc.subject
Virasoro Algebra
de
dc.subject
representation theory
en
dc.subject
Virasoro algebra
en
dc.title
Highest weight representations of the virasoro algebra
en
dc.title.alternative
Darstellungstheorie der Virasoro Algebra
de
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2018.59983
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Matthias Gerold Wödlinger
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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dc.contributor.assistant
Maresch, Gabriel
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tuw.publication.orgunit
E104 - Institut für Diskrete Mathematik und Geometrie
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dc.type.qualificationlevel
Diploma
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dc.identifier.libraryid
AC15219074
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dc.description.numberOfPages
54
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-119201
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
tuw.author.orcid
0000-0002-3872-7470
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dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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tuw.assistant.staffStatus
staff
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item.fulltext
with Fulltext
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item.cerifentitytype
Publications
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item.mimetype
application/pdf
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item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
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item.languageiso639-1
en
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item.openaccessfulltext
Open Access
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item.openairetype
master thesis
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item.grantfulltext
open
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crisitem.author.dept
E193-01 - Forschungsbereich Computer Vision
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crisitem.author.parentorg
E193 - Institut für Visual Computing and Human-Centered Technology