We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe ...

The purpose of this work is to study the relationships between admissible pairs, systems admissible and bialgebras in the category of Yetter-Drinfeld modules, as well as some properties of the Hopf algebra associated (via ...

Some Hopf algebras braided in the Yetter-Drinfeld modules category have an important role in the classification of pointed Hopf algebras. Our main goal in this work will be to characterize braided Hopf algebras in ...

Let (F,G, ◃, ▹) be a matched pair of finite groups and σ : F × F −→ (|×)G and τ : G×G −→ (|×)F two 2-cocycles. In general, the bicrossed product R = |G ∗τ σ |F is not a bialgebra, neither a braided Hopf algebra. The ...

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories ...

Let (Formula presented.) be the Drinfeld double of the bosonization (Formula presented.)(V)(Formula presented.)G of a finite-dimensional Nichols algebra (Formula presented.)(V ) over a finite group G. It is known that the ...

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 ...

In this survey, we first review some known results on the representationtheory of algebras with triangular decomposition, including the classification of the simple modules. We then discuss a recipe to construct Hopf ...

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 ...