Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2

Autores
Bruillard, Paul; Galindo, César; Hong, Seung Moon; Kashina, Yevgenia; Naidu, Deepak; Natale, Sonia Lujan; Plavnik, Julia Yael; Rowell, Eric C.
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We classify integral modular categories of dimension pq^4 and p^2q^2, where p and q are distinct primes. We show that such categories are always group-theoretical except for categories of dimension 4q^2. In these cases there are well-known examples of non-group-theoretical categories, coming from centers of Tambara-Yamagami categories and quantum groups. We show that a non-group-theoretical integral modular category of dimension 4q^2 is equivalent to either one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising from a certain quantum group.
Fil: Bruillard, Paul. Texas A&M University; Estados Unidos
Fil: Galindo, César. Universidad de Los Andes; Colombia
Fil: Hong, Seung Moon. University of Toledo; Estados Unidos
Fil: Kashina, Yevgenia. DePaul University; Estados Unidos
Fil: Naidu, Deepak. Northern Illinois University; Estados Unidos
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: Plavnik, Julia Yael. 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: Rowell, Eric C.. Texas A&M University; Estados Unidos
Materia
Fusion Category
Modular Category
Group-Theoretical 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:11336/20970
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2Bruillard, PaulGalindo, CésarHong, Seung MoonKashina, YevgeniaNaidu, DeepakNatale, Sonia LujanPlavnik, Julia YaelRowell, Eric C.Fusion CategoryModular CategoryGroup-Theoretical Fusion Categoryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We classify integral modular categories of dimension pq^4 and p^2q^2, where p and q are distinct primes. We show that such categories are always group-theoretical except for categories of dimension 4q^2. In these cases there are well-known examples of non-group-theoretical categories, coming from centers of Tambara-Yamagami categories and quantum groups. We show that a non-group-theoretical integral modular category of dimension 4q^2 is equivalent to either one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising from a certain quantum group.Fil: Bruillard, Paul. Texas A&M University; Estados UnidosFil: Galindo, César. Universidad de Los Andes; ColombiaFil: Hong, Seung Moon. University of Toledo; Estados UnidosFil: Kashina, Yevgenia. DePaul University; Estados UnidosFil: Naidu, Deepak. Northern Illinois University; Estados UnidosFil: 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: Plavnik, Julia Yael. 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: Rowell, Eric C.. Texas A&M University; Estados UnidosCanadian Mathematical Soc2014-04info: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/11336/20970Bruillard, Paul; Galindo, César; Hong, Seung Moon; Kashina, Yevgenia; Naidu, Deepak; et al.; Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2; Canadian Mathematical Soc; Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques; 57; 4; 4-2014; 721-7340008-4395CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4153/CMB-2013-042-6info:eu-repo/semantics/altIdentifier/url/https://cms.math.ca/10.4153/CMB-2013-042-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:13:05Zoai:ri.conicet.gov.ar:11336/20970instacron: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:34982025-09-10 13:13:06.055CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
title Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
spellingShingle Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
Bruillard, Paul
Fusion Category
Modular Category
Group-Theoretical Fusion Category
title_short Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
title_full Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
title_fullStr Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
title_full_unstemmed Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
title_sort Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
dc.creator.none.fl_str_mv Bruillard, Paul
Galindo, César
Hong, Seung Moon
Kashina, Yevgenia
Naidu, Deepak
Natale, Sonia Lujan
Plavnik, Julia Yael
Rowell, Eric C.
author Bruillard, Paul
author_facet Bruillard, Paul
Galindo, César
Hong, Seung Moon
Kashina, Yevgenia
Naidu, Deepak
Natale, Sonia Lujan
Plavnik, Julia Yael
Rowell, Eric C.
author_role author
author2 Galindo, César
Hong, Seung Moon
Kashina, Yevgenia
Naidu, Deepak
Natale, Sonia Lujan
Plavnik, Julia Yael
Rowell, Eric C.
author2_role author
author
author
author
author
author
author
dc.subject.none.fl_str_mv Fusion Category
Modular Category
Group-Theoretical Fusion Category
topic Fusion Category
Modular Category
Group-Theoretical 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 classify integral modular categories of dimension pq^4 and p^2q^2, where p and q are distinct primes. We show that such categories are always group-theoretical except for categories of dimension 4q^2. In these cases there are well-known examples of non-group-theoretical categories, coming from centers of Tambara-Yamagami categories and quantum groups. We show that a non-group-theoretical integral modular category of dimension 4q^2 is equivalent to either one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising from a certain quantum group.
Fil: Bruillard, Paul. Texas A&M University; Estados Unidos
Fil: Galindo, César. Universidad de Los Andes; Colombia
Fil: Hong, Seung Moon. University of Toledo; Estados Unidos
Fil: Kashina, Yevgenia. DePaul University; Estados Unidos
Fil: Naidu, Deepak. Northern Illinois University; Estados Unidos
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: Plavnik, Julia Yael. 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: Rowell, Eric C.. Texas A&M University; Estados Unidos
description We classify integral modular categories of dimension pq^4 and p^2q^2, where p and q are distinct primes. We show that such categories are always group-theoretical except for categories of dimension 4q^2. In these cases there are well-known examples of non-group-theoretical categories, coming from centers of Tambara-Yamagami categories and quantum groups. We show that a non-group-theoretical integral modular category of dimension 4q^2 is equivalent to either one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising from a certain quantum group.
publishDate 2014
dc.date.none.fl_str_mv 2014-04
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/11336/20970
Bruillard, Paul; Galindo, César; Hong, Seung Moon; Kashina, Yevgenia; Naidu, Deepak; et al.; Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2; Canadian Mathematical Soc; Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques; 57; 4; 4-2014; 721-734
0008-4395
CONICET Digital
CONICET
url http://hdl.handle.net/11336/20970
identifier_str_mv Bruillard, Paul; Galindo, César; Hong, Seung Moon; Kashina, Yevgenia; Naidu, Deepak; et al.; Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2; Canadian Mathematical Soc; Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques; 57; 4; 4-2014; 721-734
0008-4395
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4153/CMB-2013-042-6
info:eu-repo/semantics/altIdentifier/url/https://cms.math.ca/10.4153/CMB-2013-042-6
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 Canadian Mathematical Soc
publisher.none.fl_str_mv Canadian Mathematical Soc
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 12.993085

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