Quantization of algebraic invariants through Topological Quantum Field Theories

In this paper we investigate the problem of constructing Topological Quantum Field Theories (TQFTs) to quantize algebraic invariants. We exhibit necessary conditions for quantizability based on Euler characteristics. In the case of surfaces, also provide a partial answer in terms of sufficient condi...

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Detalles Bibliográficos
Autor: González Prieto, José Ángel
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/104007
Acceso en línea:https://hdl.handle.net/20.500.14352/104007
Access Level:acceso abierto
Palabra clave:TQFT
Quantization
Monoidal structure
Topological Quantum Field Theory
Representation variety
Topología
1210 Topología
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spelling Quantization of algebraic invariants through Topological Quantum Field TheoriesGonzález Prieto, José ÁngelTQFTQuantizationMonoidal structureTopological Quantum Field TheoryRepresentation varietyTopología1210 TopologíaIn this paper we investigate the problem of constructing Topological Quantum Field Theories (TQFTs) to quantize algebraic invariants. We exhibit necessary conditions for quantizability based on Euler characteristics. In the case of surfaces, also provide a partial answer in terms of sufficient conditions by means of almost-TQFTs and almost-Frobenius algebras for wide TQFTs. As an application, we show that the Poincaré polynomial of G-representation varieties is not a quantizable invariant by means of a monoidal TQFTs for any algebraic group G of positive dimension.ElsevierUniversidad Complutense de Madrid20232023-07-0120232023-07-01journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/104007reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/1040072026-06-02T12:44:21Z
dc.title.none.fl_str_mv Quantization of algebraic invariants through Topological Quantum Field Theories
title Quantization of algebraic invariants through Topological Quantum Field Theories
spellingShingle Quantization of algebraic invariants through Topological Quantum Field Theories
González Prieto, José Ángel
TQFT
Quantization
Monoidal structure
Topological Quantum Field Theory
Representation variety
Topología
1210 Topología
title_short Quantization of algebraic invariants through Topological Quantum Field Theories
title_full Quantization of algebraic invariants through Topological Quantum Field Theories
title_fullStr Quantization of algebraic invariants through Topological Quantum Field Theories
title_full_unstemmed Quantization of algebraic invariants through Topological Quantum Field Theories
title_sort Quantization of algebraic invariants through Topological Quantum Field Theories
dc.creator.none.fl_str_mv González Prieto, José Ángel
author González Prieto, José Ángel
author_facet González Prieto, José Ángel
author_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv TQFT
Quantization
Monoidal structure
Topological Quantum Field Theory
Representation variety
Topología
1210 Topología
topic TQFT
Quantization
Monoidal structure
Topological Quantum Field Theory
Representation variety
Topología
1210 Topología
description In this paper we investigate the problem of constructing Topological Quantum Field Theories (TQFTs) to quantize algebraic invariants. We exhibit necessary conditions for quantizability based on Euler characteristics. In the case of surfaces, also provide a partial answer in terms of sufficient conditions by means of almost-TQFTs and almost-Frobenius algebras for wide TQFTs. As an application, we show that the Poincaré polynomial of G-representation varieties is not a quantizable invariant by means of a monoidal TQFTs for any algebraic group G of positive dimension.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-07-01
2023
2023-07-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/104007
url https://hdl.handle.net/20.500.14352/104007
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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