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. ...

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 ...

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 ...

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 ...

We present new Hopf algebras with the dual Chevalley property by determining all semisimple Hopf algebras Morita-equivalent to a group algebra over a finite group, for a list of groups supporting a non-trivial finite-dimensional ...

This work aims to continue with the work started in the Article Braided Zesting and its Applications, the original and main result of this work is the classification of the braided zestings of fusion categories obtained ...

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 ...

"En este trabajo determinamos la obstruccion a la existencia de una estructura trenzada para una Categoría de Fusion Punteada. Damos además una solución explícita de la ecuacion hexagonal en caso de que exista. Con este ...

"Parametrizamos las extesiones modulares minimales para categorias de fusion super-Tanakianas en terminos de grupos de cohomologia en grado 2 y 3. Para esto, usamos los procesos de equivariantización, de-equivariantización ...