Geodesic
Classification of Integral Modular Categories of Frobenius–Perron Dimension pq 4 and p 2 q 2
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 721-734

Voir la notice de l'article provenant de la source Cambridge

DOI

We classify integral modular categories of dimension $p{{q}^{4}}$ and ${{p}^{2}}{{q}^{2}}$ , where $p$ and $q$ are distinct primes. We show that such categories are always group-theoretical, except for categories of dimension $4{{q}^{2}}$ . 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-grouptheoretical integral modular category of dimension $4{{q}^{2}}$ is either equivalent to one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising froma certain quantum group.
DOI : 10.4153/CMB-2013-042-6
Mots-clés : 18D10, modular categories, fusion categories 
Bruillard, Paul; Galindo, Cásar; Hong, Seung-Moon; Kashina, Yevgenia; Naidu, Deepak; Natale, Sonia; Plavnik, Julia Yael; Rowell, Eric C. Classification of Integral Modular Categories of Frobenius–Perron Dimension pq 4 and p 2 q 2. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 721-734. doi: 10.4153/CMB-2013-042-6
@article{10_4153_CMB_2013_042_6,
     author = {Bruillard, Paul and Galindo, C\'asar and Hong, Seung-Moon and Kashina, Yevgenia and Naidu, Deepak and Natale, Sonia and Plavnik, Julia Yael and Rowell, Eric C.},
     title = {Classification of {Integral} {Modular} {Categories} of {Frobenius{\textendash}Perron} {Dimension} pq 4 and p 2 q 2},
     journal = {Canadian mathematical bulletin},
     pages = {721--734},
     year = {2014},
     volume = {57},
     number = {4},
     doi = {10.4153/CMB-2013-042-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-042-6/}
}
TY  - JOUR
AU  - Bruillard, Paul
AU  - Galindo, Cásar
AU  - Hong, Seung-Moon
AU  - Kashina, Yevgenia
AU  - Naidu, Deepak
AU  - Natale, Sonia
AU  - Plavnik, Julia Yael
AU  - Rowell, Eric C.
TI  - Classification of Integral Modular Categories of Frobenius–Perron Dimension pq 4 and p 2 q 2
JO  - Canadian mathematical bulletin
PY  - 2014
SP  - 721
EP  - 734
VL  - 57
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-042-6/
DO  - 10.4153/CMB-2013-042-6
ID  - 10_4153_CMB_2013_042_6
ER  - 
%0 Journal Article
%A Bruillard, Paul
%A Galindo, Cásar
%A Hong, Seung-Moon
%A Kashina, Yevgenia
%A Naidu, Deepak
%A Natale, Sonia
%A Plavnik, Julia Yael
%A Rowell, Eric C.
%T Classification of Integral Modular Categories of Frobenius–Perron Dimension pq 4 and p 2 q 2
%J Canadian mathematical bulletin
%D 2014
%P 721-734
%V 57
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-042-6/
%R 10.4153/CMB-2013-042-6
%F 10_4153_CMB_2013_042_6

Cité par Sources :