Möller, Sven (2016)
A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung
Kurzbeschreibung (Abstract)
In this thesis we develop an orbifold theory for a finite, cyclic group G acting on a suitably regular, holomorphic vertex operator algebra V. To this end we describe the fusion algebra of the fixed-point vertex operator subalgebra V^G and show that V^G has group-like fusion. Then we solve the extension problem for vertex operator algebras with group-like fusion.
We use these results to construct five new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds, contributing to the classification of the V_1-structures of suitably regular, holomorphic vertex operator algebras of central charge 24.
As another application we present the BRST construction of ten Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight.
| Typ des Eintrags: | Dissertation | ||||
|---|---|---|---|---|---|
| Erschienen: | 2016 | ||||
| Autor(en): | Möller, Sven | ||||
| Art des Eintrags: | Erstveröffentlichung | ||||
| Titel: | A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications | ||||
| Sprache: | Englisch | ||||
| Referenten: | Scheithauer, Prof. Dr. Nils ; Möller, Prof. Dr. Martin ; Höhn, Prof. Dr. Gerald | ||||
| Publikationsjahr: | 29 November 2016 | ||||
| Ort: | Darmstadt | ||||
| Datum der mündlichen Prüfung: | 15 September 2016 | ||||
| URL / URN: | http://tuprints.ulb.tu-darmstadt.de/5821 | ||||
| Kurzbeschreibung (Abstract): | In this thesis we develop an orbifold theory for a finite, cyclic group G acting on a suitably regular, holomorphic vertex operator algebra V. To this end we describe the fusion algebra of the fixed-point vertex operator subalgebra V^G and show that V^G has group-like fusion. Then we solve the extension problem for vertex operator algebras with group-like fusion. We use these results to construct five new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds, contributing to the classification of the V_1-structures of suitably regular, holomorphic vertex operator algebras of central charge 24. As another application we present the BRST construction of ten Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight. |
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| Alternatives oder übersetztes Abstract: |
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| Freie Schlagworte: | vertex operator algebras, orbifold theory, extension problem, generalised Kac-Moody algebras | ||||
| URN: | urn:nbn:de:tuda-tuprints-58215 | ||||
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Algebra 04 Fachbereich Mathematik > Algebra > Unendlichdimensionale Lie-Algebren, Vertexalgebren, Automorphe Formen |
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| Hinterlegungsdatum: | 04 Dez 2016 20:55 | ||||
| Letzte Änderung: | 15 Feb 2021 19:08 | ||||
| PPN: | |||||
| Referenten: | Scheithauer, Prof. Dr. Nils ; Möller, Prof. Dr. Martin ; Höhn, Prof. Dr. Gerald | ||||
| Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: | 15 September 2016 | ||||
| Export: | |||||
| Suche nach Titel in: | TUfind oder in Google | ||||
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