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On the equivalence of module categories over a group-theoretical fusion category
(Natl Acad Sci Ukraine, 2017-06)
We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category C to be equivalent. This concludes the classification of such ...
On fusion rules and solvability of a fusion category
(De Gruyter, 2017-01)
We address the question whether or not the condition on a fusion category being solvable is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from ...
On the Classification of Almost Square-Free Modular Categories
(Springer, 2017-11)
Let (Formula presented.) be a modular category of Frobenius-Perron dimension dqn, where q > 2 is a prime number and d is a square-free integer. We show that (Formula presented.) must be integral and nilpotent and therefore ...
On weakly group-theoretical non-degenerate braided fusion categories
(European Mathematical Society, 2014-01)
We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. ...
Graphs attached to simple Frobenius-Perron dimensions of an integral fusion category
(Springer Wien, 2016-04)
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 ...
On fusion categories with few irreducible degrees
(Mathematical Sciences Publishers, 2012-08)
We prove some results on the structure of certain classes of integral fusion categories and semisimple Hopf algebras under restrictions on the set of their irreducible degrees.
Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
(Canadian Mathematical Soc, 2014-04)
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 ...
Frobenius property for fusion categories of small integral dimension
(World Scientific, 2015-03)
Let k be an algebraically closed field of characteristic zero. In this paper, we prove that fusion categories of Frobenius–Perron dimensions 84 and 90 are of Frobenius type. Combining this with previous results in the ...
Grafos de Frobenius-Perron para categorías de fusión
(2015-03)
Sea C una categoría de fusión íntegra, en este trabajo se estudian algunos grafos, llamados el grafo primo y el grafo común divisor, relacionados con las dimensiones de Frobenius-Perron de los objetos simples de C. Estos ...
Derived counterparts of fusion categories of quantum groups
(UniandesDoctorado en MatemáticasFacultad de CienciasDepartamento de Matemáticas, 2017)
"En esta tesis, se estudian versiones derivadas de la categoría de fusión asociada con el grupo cuántico de Lusztig U_q. Las categorías obtenidas no son semisimples pero recuperan el anillo de fusión usual cuando calculamos ...