On fusion rules and solvability of a fusion category

Autores
Natale, Sonia Lujan; Escañuela Gonzalez, Melisa Gisselle
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We address the question whether or not the condition on a fusion category being solvable is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from representations of semisimple Hopf algebras associated to exact factorizations of the symmetric and alternating groups. In the context of spherical fusion categories, we also consider the invariant provided by the S-matrix of the Drinfeld center and show that this invariant does determine the solvability of a fusion category provided it is 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
Fil: Escañuela Gonzalez, Melisa Gisselle. 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
fusion category
solvability
fusion rules
braided fusion category
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:11336/59792
Acceder
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spelling On fusion rules and solvability of a fusion categoryNatale, Sonia LujanEscañuela Gonzalez, Melisa Gissellefusion categorysolvabilityfusion rulesbraided fusion categoryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We address the question whether or not the condition on a fusion category being solvable is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from representations of semisimple Hopf algebras associated to exact factorizations of the symmetric and alternating groups. In the context of spherical fusion categories, we also consider the invariant provided by the S-matrix of the Drinfeld center and show that this invariant does determine the solvability of a fusion category provided it is 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; ArgentinaFil: Escañuela Gonzalez, Melisa Gisselle. 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; ArgentinaDe Gruyter2017-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/59792Natale, Sonia Lujan; Escañuela Gonzalez, Melisa Gisselle; On fusion rules and solvability of a fusion category; De Gruyter; Journal Of Group Theory; 20; 1; 1-2017; 133-1671433-5883CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1515/jgth-2016-0020info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/jgth.2017.20.issue-1/jgth-2016-0020/jgth-2016-0020.xmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:10:35Zoai:ri.conicet.gov.ar:11336/59792instacron: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:34982025-09-29 10:10:35.919CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On fusion rules and solvability of a fusion category
title On fusion rules and solvability of a fusion category
spellingShingle On fusion rules and solvability of a fusion category
Natale, Sonia Lujan
fusion category
solvability
fusion rules
braided fusion category
title_short On fusion rules and solvability of a fusion category
title_full On fusion rules and solvability of a fusion category
title_fullStr On fusion rules and solvability of a fusion category
title_full_unstemmed On fusion rules and solvability of a fusion category
title_sort On fusion rules and solvability of a fusion category
dc.creator.none.fl_str_mv Natale, Sonia Lujan
Escañuela Gonzalez, Melisa Gisselle
author Natale, Sonia Lujan
author_facet Natale, Sonia Lujan
Escañuela Gonzalez, Melisa Gisselle
author_role author
author2 Escañuela Gonzalez, Melisa Gisselle
author2_role author
dc.subject.none.fl_str_mv fusion category
solvability
fusion rules
braided fusion category
topic fusion category
solvability
fusion rules
braided fusion category
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 address the question whether or not the condition on a fusion category being solvable is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from representations of semisimple Hopf algebras associated to exact factorizations of the symmetric and alternating groups. In the context of spherical fusion categories, we also consider the invariant provided by the S-matrix of the Drinfeld center and show that this invariant does determine the solvability of a fusion category provided it is 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
Fil: Escañuela Gonzalez, Melisa Gisselle. 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 address the question whether or not the condition on a fusion category being solvable is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from representations of semisimple Hopf algebras associated to exact factorizations of the symmetric and alternating groups. In the context of spherical fusion categories, we also consider the invariant provided by the S-matrix of the Drinfeld center and show that this invariant does determine the solvability of a fusion category provided it is group-theoretical.
publishDate 2017
dc.date.none.fl_str_mv 2017-01
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/11336/59792
Natale, Sonia Lujan; Escañuela Gonzalez, Melisa Gisselle; On fusion rules and solvability of a fusion category; De Gruyter; Journal Of Group Theory; 20; 1; 1-2017; 133-167
1433-5883
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59792
identifier_str_mv Natale, Sonia Lujan; Escañuela Gonzalez, Melisa Gisselle; On fusion rules and solvability of a fusion category; De Gruyter; Journal Of Group Theory; 20; 1; 1-2017; 133-167
1433-5883
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1515/jgth-2016-0020
info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/jgth.2017.20.issue-1/jgth-2016-0020/jgth-2016-0020.xml
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
application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
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
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score 13.069144

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