6 papers
On Low-Dimensional Locally Compact Quantum Groups
Stefaan Vaes, Leonid Vainerman
Continuing our research on extensions of locally compact quantum groups, we give a classification of all cocycle matched pairs of Lie algebras in small dimensions and prove that al…
Extensions of locally compact quantum groups and the bicrossed product construction
Stefaan Vaes, Leonid Vainerman
In the framework of locally compact quantum groups, we study cocycle actions. We develop the cocycle bicrossed product construction, starting from a matched pair of locally compact…
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…
A Galois correspondence for II_1 factors and quantum groupoids
Dmitri Nikshych, Leonid Vainerman
We establish a Galois correspondence for finite quantum groupoid actions on II_1 factors and show that every finite index and finite depth subfactor is an intermediate subalgebra o…
Algebraic Versions of a Finite-Dimensional Quantum Groupoid
D. Nikshych, L. Vainerman
We establish the equivalence of three versions of a finite dimensional quantum groupoid: a generalized Kac algebra introduced by T. Yamanouchi, a weak -Hopf algebra introduced…