Sonia Natale

On group theoretical Hopf algebras and exact factorizations of finite groups

Abstract We show that a semisimple Hopf algebra A is group theoretical if and only if its Drinfeld double is a twisting of the Dijkgraaf–Pasquier–Roche quasi-Hopf algebra D ω ( Σ ), for some finite group Σ and some ω ∈ Z 3 ( Σ , k × ). We show that semisimple Hopf algebras obtained as bicrossed products from an exact factorization of a finite group Σ are group theoretical. We also describe their Drinfeld double as a twisting of D ω ( Σ ), for an appropriate 3-cocycle ω coming from the Kac exact sequence.

Fusion rules of equivariantizations of fusion categories

We determine the fusion rules of the equivariantization of a fusion category

Hopf Algebras of Dimension 12

\mathcal{C}

Faithful simple objects, orders and gradings of fusion categories

under the action of a finite group

On Semisimple Hopf Algebras of Dimension pq2, II

G

On weakly group-theoretical non-degenerate braided fusion categories

in terms of the fusion rules of

Braided Hopf algebras arising from matched pairs of groups

\mathcal{C}

Frobenius property for fusion categories of small integral dimension

and group-theoretical data associated to the group action. As an application we obtain a formula for the fusion rules in an equivariantization of a pointed fusion category in terms of group-theoretical data. This entails a description of the fusion rules in any braided group-theoretical fusion category.

Classification of Integral Modular Categories of Frobenius--Perron Dimension and

We conclude the classification of Hopf algebras of dimension 12 over an algebraically closed field of characteristic zero.

Solvability of a Class of Braided Fusion Categories

We establish some relations between the orders of simple objects in a fusion category and the structure of its universal grading group. We consider fusion categories which have a faithful simple object and show that its universal grading group must be cyclic. As for the converse, we prove that a braided nilpotent fusion category with cyclic universal grading group always has a faithful simple object. We study the universal grading of fusion categories with generalized Tambara-Yamagami fusion rules. As an application, we classify modular categories in this class and describe the modularizations of braided Tambara-Yamagami fusion categories.