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dc.contributor.author
Natale, Sonia Lujan
dc.contributor.author
Pacheco Rodriguez, Edwin Fernando
dc.date.available
2018-02-27T19:46:19Z
dc.date.issued
2016-04
dc.identifier.citation
Natale, Sonia Lujan; Pacheco Rodriguez, Edwin Fernando; Graphs attached to simple Frobenius-Perron dimensions of an integral fusion category; Springer Wien; Monatshefete Fur Mathematik; 179; 4; 4-2016; 615-649
dc.identifier.issn
0026-9255
dc.identifier.uri
http://hdl.handle.net/11336/37315
dc.description.abstract
Let (Formula presented.) be an integral fusion category. We study some graphs, called the prime graph and the common divisor graph, related to the Frobenius-Perron dimensions of simple objects in the category (Formula presented.) , that extend the corresponding graphs associated to the irreducible character degrees and the conjugacy class sizes of a finite group. We describe these graphs in several cases, among others, when (Formula presented.) is an equivariantization under the action of a finite group, a (Formula presented.) -step nilpotent fusion category, and the representation category of a twisted quantum double. We prove generalizations of known results on the number of connected components of the corresponding graphs for finite groups in the context of braided fusion categories. In particular, we show that if (Formula presented.) is any integral non-degenerate braided fusion category, then the prime graph of (Formula presented.) has at most (Formula presented.) connected components, and it has at most (Formula presented.) connected components if (Formula presented.) is in addition solvable. As an application we prove a classification result for weakly integral braided fusion categories all of whose simple objects have prime power Frobenius-Perron dimension.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer Wien
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Braided Fusion Category
dc.subject
Equivariantization
dc.subject
Frobenius-Perron Dimension
dc.subject
Frobenius-Perron Graph
dc.subject
Fusion Category
dc.subject
Modular Category
dc.subject
Solvability
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Graphs attached to simple Frobenius-Perron dimensions of an integral fusion category
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-02-27T14:17:46Z
dc.journal.volume
179
dc.journal.number
4
dc.journal.pagination
615-649
dc.journal.pais
Austria
dc.journal.ciudad
Viena
dc.description.fil
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
dc.description.fil
Fil: Pacheco Rodriguez, Edwin Fernando. 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
dc.journal.title
Monatshefete Fur Mathematik
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00605-015-0734-7
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00605-015-0734-7
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