1. CMB 2014 (vol 57 pp. 721)
||Classification of Integral Modular Categories of Frobenius--Perron Dimension $pq^4$ and $p^2q^2$|
We classify integral modular categories of dimension $pq^4$ and $p^2q^2$,
$p$ and $q$ are distinct primes. We show that such categories are always
group-theoretical except for categories of dimension $4q^2$.
In these cases there are
well-known examples of non-group-theoretical categories, coming from
Tambara-Yamagami categories and quantum groups. We show that a
non-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 a
certain quantum group.
Keywords:modular categories, fusion categories
2. CMB 2013 (vol 57 pp. 506)
||On Braided and Ribbon Unitary Fusion Categories|
We prove that every braiding over a unitary fusion category is
unitary and every unitary braided fusion category admits a unique
unitary ribbon structure.
Keywords:fusion categories, braided categories, modular categories
Categories:20F36, 16W30, 18D10