A class of prime fusion categories of dimension 2^N

Autores
Jingcheng, Dong; Natale, Sonia Lujan; Hua, Sun
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study a class of strictly weakly integral fusion categories I_{N,ζ}, where N≥1 is a natural number and ζ is a 2^Nth root of unity, that we call N-Ising fusion categories. An N-Ising fusion category has Frobenius-Perron dimension 2^{N+1} and is a graded extension of a pointed fusion category of rank 2 by the cyclic group of order Z_{2^N}. We show that every braided N-Ising fusion category is prime and also that there exists a slightly degenerate N-Ising braided fusion category for all N>2. We also prove a structure result for braided extensions of a rank 2 pointed fusion category in terms of braided N-Ising fusion categories.
Fil: Jingcheng, Dong. Nanjing University Of Information Science & Technology; China
Fil: Natale, Sonia Lujan. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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: Hua, Sun. Yangzhou University; China
Materia
FUSION CATEGORY
BRAIDES FUSION CATEGORY
GROUP EXTENSION
ISING 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:11336/172764
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/172764
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling A class of prime fusion categories of dimension 2^NJingcheng, DongNatale, Sonia LujanHua, SunFUSION CATEGORYBRAIDES FUSION CATEGORYGROUP EXTENSIONISING CATEGORYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study a class of strictly weakly integral fusion categories I_{N,ζ}, where N≥1 is a natural number and ζ is a 2^Nth root of unity, that we call N-Ising fusion categories. An N-Ising fusion category has Frobenius-Perron dimension 2^{N+1} and is a graded extension of a pointed fusion category of rank 2 by the cyclic group of order Z_{2^N}. We show that every braided N-Ising fusion category is prime and also that there exists a slightly degenerate N-Ising braided fusion category for all N>2. We also prove a structure result for braided extensions of a rank 2 pointed fusion category in terms of braided N-Ising fusion categories.Fil: Jingcheng, Dong. Nanjing University Of Information Science & Technology; ChinaFil: Natale, Sonia Lujan. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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: Hua, Sun. Yangzhou University; ChinaUniversity of Albany2021-02info: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/11336/172764Jingcheng, Dong; Natale, Sonia Lujan; Hua, Sun; A class of prime fusion categories of dimension 2^N; University of Albany; New York Journal of Mathematics; 27; 2-2021; 141-1631076-9803CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://nyjm.albany.edu/j/2021/27-5p.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T12:29:49Zoai:ri.conicet.gov.ar:11336/172764instacron: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:34982025-10-29 12:29:50.28CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A class of prime fusion categories of dimension 2^N
title A class of prime fusion categories of dimension 2^N
spellingShingle A class of prime fusion categories of dimension 2^N
Jingcheng, Dong
FUSION CATEGORY
BRAIDES FUSION CATEGORY
GROUP EXTENSION
ISING CATEGORY
title_short A class of prime fusion categories of dimension 2^N
title_full A class of prime fusion categories of dimension 2^N
title_fullStr A class of prime fusion categories of dimension 2^N
title_full_unstemmed A class of prime fusion categories of dimension 2^N
title_sort A class of prime fusion categories of dimension 2^N
dc.creator.none.fl_str_mv Jingcheng, Dong
Natale, Sonia Lujan
Hua, Sun
author Jingcheng, Dong
author_facet Jingcheng, Dong
Natale, Sonia Lujan
Hua, Sun
author_role author
author2 Natale, Sonia Lujan
Hua, Sun
author2_role author
author
dc.subject.none.fl_str_mv FUSION CATEGORY
BRAIDES FUSION CATEGORY
GROUP EXTENSION
ISING CATEGORY
topic FUSION CATEGORY
BRAIDES FUSION CATEGORY
GROUP EXTENSION
ISING 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 study a class of strictly weakly integral fusion categories I_{N,ζ}, where N≥1 is a natural number and ζ is a 2^Nth root of unity, that we call N-Ising fusion categories. An N-Ising fusion category has Frobenius-Perron dimension 2^{N+1} and is a graded extension of a pointed fusion category of rank 2 by the cyclic group of order Z_{2^N}. We show that every braided N-Ising fusion category is prime and also that there exists a slightly degenerate N-Ising braided fusion category for all N>2. We also prove a structure result for braided extensions of a rank 2 pointed fusion category in terms of braided N-Ising fusion categories.
Fil: Jingcheng, Dong. Nanjing University Of Information Science & Technology; China
Fil: Natale, Sonia Lujan. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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: Hua, Sun. Yangzhou University; China
description We study a class of strictly weakly integral fusion categories I_{N,ζ}, where N≥1 is a natural number and ζ is a 2^Nth root of unity, that we call N-Ising fusion categories. An N-Ising fusion category has Frobenius-Perron dimension 2^{N+1} and is a graded extension of a pointed fusion category of rank 2 by the cyclic group of order Z_{2^N}. We show that every braided N-Ising fusion category is prime and also that there exists a slightly degenerate N-Ising braided fusion category for all N>2. We also prove a structure result for braided extensions of a rank 2 pointed fusion category in terms of braided N-Ising fusion categories.
publishDate 2021
dc.date.none.fl_str_mv 2021-02
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/11336/172764
Jingcheng, Dong; Natale, Sonia Lujan; Hua, Sun; A class of prime fusion categories of dimension 2^N; University of Albany; New York Journal of Mathematics; 27; 2-2021; 141-163
1076-9803
CONICET Digital
CONICET
url http://hdl.handle.net/11336/172764
identifier_str_mv Jingcheng, Dong; Natale, Sonia Lujan; Hua, Sun; A class of prime fusion categories of dimension 2^N; University of Albany; New York Journal of Mathematics; 27; 2-2021; 141-163
1076-9803
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://nyjm.albany.edu/j/2021/27-5p.pdf
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 University of Albany
publisher.none.fl_str_mv University of Albany
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 12.589754

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