Related papers: Yetter-Drinfeld modules over weak Hopf algebras an…

In this paper we prove a formula that relates M\"uger's centralizer in the category of representations of a factorizable Hopf algebra to the notion of Hopf kernel of a representation of the dual Hopf algebra. Using this relation we obtain a…

We classify all groups G and all pairs (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the support of the direct sum of V and W generates G, the square of the braiding between V and W is not the identity, and the Nichols…

Let H be a coFrobenius Hopf algebra over a field k. Let A be a right H-comodule algebra over k. We recall that the category of right H-comodules admits a certain model structure whose homotopy category is equivalent to the stable category…

In Rev. Math. Phys. 4 (1997) 785 we study Hilbert-C* systems {F,G} where the fixed point algebra A has nontrivial center Z and where A'\cap F=Z is satisfied. The corresponding category of all canonical endomorphisms of A contains…

By building on the notions of internal projective and injective objects in a module category introduced by Douglas, Schommer-Pries, and Snyder, we extend the reconstruction theory for module categories of Etingof and Ostrik. More…

In this paper, we define and study weak monoidal Hom-Hopf algebras, which generalize both weak Hopf algebras and monoidal Hom-Hopf algebras. If $H$ is a weak monoidal Hom-Hopf algebra with bijective antipode and let $Aut_{wmHH}(H)$ be the…

This paper is a contribution to the construction of non-semisimple modular categories. We establish when M\"uger centralizers inside non-semisimple modular categories are also modular. As a consequence, we obtain conditions under which…

It is known that finite crossed modules provide premodular tensor categories. These categories are in fact modularizable. We construct the modularization and show that it is equivalent to the module category of a finite Drinfeld double.

Given a Hopf algebra $H$, Brzezi\'nski and Militaru have shown that each braided commutative Yetter-Drinfeld $H$-module algebra $A$ gives rise to an associative $A$-bialgebroid structure on the smash product algebra $A \sharp H$. They also…

We prove that a finite-dimensional Hopf algebra with the dual Chevalley Property over a field of characteristic zero is quasi-isomorphic to a Radford-Majid bosonization whenever the third Hochschild cohomology group in the category of…

If H is a finite dimensional Hopf algebra, C. Cibils and M. Rosso found an algebra X having the property that Hopf bimodules over H^* coincide with left X-modules. We find two other algebras, Y and Z, having the same property; namely, Y is…

Using crossed homomorphisms, we show that the category of weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs) is a left module category over the monoidal category of representations of Lie…

In the first part we recall two famous sources of solutions to the Yang-Baxter equation -- R-matrices and Yetter-Drinfel$'$d (=YD) modules -- and an interpretation of the former as a particular case of the latter. We show that this result…

We give an interpretation of Yetter's Invariant of manifolds $M$ in terms of the homotopy type of the function space $TOP(M,B(G))$, where $G$ is a crossed module and $B(G)$ is its classifying space. From this formulation, there follows that…

We extend the Larson-Sweedler theorem to weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We show that the category of modules over a weak Hopf…

We propose a framework for producing interesting subcategories of the category ${}_A\mathsf{Mod}$ of left $A$-modules, where $A$ is an associative algebra over a field $k$. The construction is based on the composition, $Y$, of the Yoneda…

We characterize braided commutative Yetter-Drinfeld $C^*$-algebras over weak Hopf $C^*$-algebras in categorical terms. Using this, we then study quotient type coideal subalgebras of a given weak Hopf $C^*$-algebra $\mathcal G$ and coideal…

We classify finite pointed braided tensor categories admitting a fiber functor in terms of bilinear forms on symmetric Yetter-Drinfeld modules over abelian groups. We describe the groupoid formed by braided equivalences of such categories…

In this paper we introduce the theory of multiplication alteration by two-cocycles for nonassociative structures like nonassociative bimonoids with left (right) division. Also we explore the connections between Yetter-Drinfeld modules for…

Given a finite dimensional Hopf algebra H and an exact indecomposable module category M over Rep(H), we explicitly compute the adjoint algebra A_M as an object in the category of Yetter-Drinfeld modules over H, and the space of class…