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math.QA2000
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…
math.QA2000
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…
math.QA2000
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…