A class of prime fusion categories of dimension 2^N
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 ra...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/172764 |
| Acceso en línea: | http://hdl.handle.net/11336/172764 |
| Access Level: | acceso abierto |
| Palabra clave: | FUSION CATEGORY BRAIDES FUSION CATEGORY GROUP EXTENSION ISING CATEGORY https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
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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 Técnicas2024-05-08T14:11:52Zoai: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:34982024-05-08 14:11:52.48CONICET 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 https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| 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 https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| topic |
FUSION CATEGORY BRAIDES FUSION CATEGORY GROUP EXTENSION ISING CATEGORY https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| 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/ |
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openAccess |
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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application/pdf application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
University of Albany |
| publisher.none.fl_str_mv |
University of Albany |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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