On weakly group-theoretical non-degenerate braided fusion categories

Autores
Natale, Sonia Lujan
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable nondegenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theoretical or solvable in terms of the factorization of its Frobenius-Perron dimension and the Frobenius-Perron dimensions of its simple objects. As an application, we prove that every non-degenerate braided fusion category whose Frobenius-Perron dimension is a natural number less than 1800, or an odd natural number less than 33075, is weakly group-theoretical.
Fil: Natale, Sonia Lujan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
Braided fusion category
braidedG-crossed fusion category
Tannakian category
Witt class
solvability
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/31948
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/31948
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling On weakly group-theoretical non-degenerate braided fusion categoriesNatale, Sonia LujanBraided fusion categorybraidedG-crossed fusion categoryTannakian categoryWitt classsolvabilityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable nondegenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theoretical or solvable in terms of the factorization of its Frobenius-Perron dimension and the Frobenius-Perron dimensions of its simple objects. As an application, we prove that every non-degenerate braided fusion category whose Frobenius-Perron dimension is a natural number less than 1800, or an odd natural number less than 33075, is weakly group-theoretical.Fil: Natale, Sonia Lujan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaEuropean Mathematical Society2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/31948On weakly group-theoretical non-degenerate braided fusion categories; European Mathematical Society; Journal of Noncommutative Geometry; 8; 4; 1-2014; 1043-10601661-6952CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1301.6078info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:14:55Zoai:ri.conicet.gov.ar:11336/31948instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:14:56.145CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On weakly group-theoretical non-degenerate braided fusion categories
title On weakly group-theoretical non-degenerate braided fusion categories
spellingShingle On weakly group-theoretical non-degenerate braided fusion categories
Natale, Sonia Lujan
Braided fusion category
braidedG-crossed fusion category
Tannakian category
Witt class
solvability
title_short On weakly group-theoretical non-degenerate braided fusion categories
title_full On weakly group-theoretical non-degenerate braided fusion categories
title_fullStr On weakly group-theoretical non-degenerate braided fusion categories
title_full_unstemmed On weakly group-theoretical non-degenerate braided fusion categories
title_sort On weakly group-theoretical non-degenerate braided fusion categories
dc.creator.none.fl_str_mv Natale, Sonia Lujan
author Natale, Sonia Lujan
author_facet Natale, Sonia Lujan
author_role author
dc.subject.none.fl_str_mv Braided fusion category
braidedG-crossed fusion category
Tannakian category
Witt class
solvability
topic Braided fusion category
braidedG-crossed fusion category
Tannakian category
Witt class
solvability
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable nondegenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theoretical or solvable in terms of the factorization of its Frobenius-Perron dimension and the Frobenius-Perron dimensions of its simple objects. As an application, we prove that every non-degenerate braided fusion category whose Frobenius-Perron dimension is a natural number less than 1800, or an odd natural number less than 33075, is weakly group-theoretical.
Fil: Natale, Sonia Lujan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable nondegenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theoretical or solvable in terms of the factorization of its Frobenius-Perron dimension and the Frobenius-Perron dimensions of its simple objects. As an application, we prove that every non-degenerate braided fusion category whose Frobenius-Perron dimension is a natural number less than 1800, or an odd natural number less than 33075, is weakly group-theoretical.
publishDate 2014
dc.date.none.fl_str_mv 2014-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/31948
On weakly group-theoretical non-degenerate braided fusion categories; European Mathematical Society; Journal of Noncommutative Geometry; 8; 4; 1-2014; 1043-1060
1661-6952
CONICET Digital
CONICET
url http://hdl.handle.net/11336/31948
identifier_str_mv On weakly group-theoretical non-degenerate braided fusion categories; European Mathematical Society; Journal of Noncommutative Geometry; 8; 4; 1-2014; 1043-1060
1661-6952
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1301.6078
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846083297280524288
score 13.22299

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