12 papers · 1 filter
On twisting of finite-dimensional Hopf algebras
Eli Aljadeff, Pavel Etingof, Shlomo Gelaki +1
In this paper we study the properties of Drinfeld's twisting for finite-dimensional Hopf algebras. We determine how the integral of the dual to a unimodular Hopf algebra change…
On the structure of weak Hopf algebras
Dmitri Nikshych
We study the group of group-like elements of a weak Hopf algebra and derive an analogue of Radford's formula for the fourth power of the antipode S, which implies that the antipode…
Vertex-IRF transformations and quantization of dynamical r-matrices
Pavel Etingof, Dmitri Nikshych
Motivated by the correspondence between the vertex and IRF models in statistical mechanics, we define and study a notion of vertex-IRF transformation for dynamical twists that gene…
Dynamical twists in group algebras
Pavel Etingof, Dmitri Nikshych
We classify dynamical twists in group algebras of finite groups. Namely, we set up a bijective correspondence between gauge equivalence classes of dynamical twists (which are solut…
Invariants of Knots and 3-manifolds from Quantum Groupoids
Dmitri Nikshych, Vladimir Turaev, Leonid Vainerman
We use categories of representations of finite dimensional quantum groupoids (weak Hopf algebras) to construct ribbon and modular categories that give rise to invariants of knots a…
Finite Quantum Groupoids and Their Applications
Dmitri Nikshych, Leonid Vainerman
We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformat…