Classification of Integral Modular Categories of Frobenius--Perron Dimension $pq^4$ and $p^2q^2$

Canadian mathematical bulletin

Julia Yael Plavnik⁴  Eric C. Rowell⁵  Seung-Moon Hong¹  Paul Bruillard⁵  Deepak Naidu³  Yevgenia Kashina⁶  César Galindo²  Sonia Natale⁴ 

[1] Department of Mathematics and Statistics, University of Toledo, Ohio 43606, USA;Departamento de matemáticas, Universidad de los Andes, Bogotá, Colombia;Department of Mathematical Sciences, Northern Illinois Universit, DeKalb, Illinois 60115, USA;Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM--CONICET, Córdoba, Argentina;Department of Mathematics, Texas A$&$M University, College Station, Texas 77843, USA;Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614, USA

关键词: modular categories;    fusion categories;   

DOI  :  10.4153/CMB-2013-042-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 alwaysgroup-theoretical except for categories of dimension $4q^2$.In these cases there arewell-known examples of non-group-theoretical categories, coming from centers ofTambara-Yamagami categories and quantum groups. We show that anon-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 acertain quantum group.

【 授权许可】

Unknown