1. CMB Online first
|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 $p^2q^2$, where $p$ 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 centers of 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
3. CMB 2004 (vol 47 pp. 321)
|Classifying Spaces for Monoidal Categories Through Geometric Nerves |
The usual constructions of classifying spaces for monoidal categories produce CW-complexes with many cells that, moreover, do not have any proper geometric meaning. However, geometric nerves of monoidal categories are very handy simplicial sets whose simplices have a pleasing geometric description: they are diagrams with the shape of the 2-skeleton of oriented standard simplices. The purpose of this paper is to prove that geometric realizations of geometric nerves are classifying spaces for monoidal categories.
Keywords:monoidal category, pseudo-simplicial category,, simplicial set, classifying space, homotopy type
Categories:18D10, 18G30, 55P15, 55P35, 55U40