78 citations · 350 across the 20 of their papers we have counts for
14 papers · 1 filter
Oriented Closed Polyhedral Maps and the Kitaev Model
Kornél Szlachányi
A kind of combinatorial map, called arrow presentation, is proposed to encode the data of the oriented closed polyhedral complexes on which the Hopf algebraic Kitaev model live…
Skew-monoidal categories and bialgebroids
Kornel Szlachanyi
Skew-monoidal categories arise when the associator and the left and right units of a monoidal category are, in a specific way, not invertible. We prove that the closed skew-monoida…
Fiber functors, monoidal sites and Tannaka duality for bialgebroids
K. Szlachanyi
What are the fiber functors on small additive monoidal categories C which are not abelian? We give an answer which leads to a new Tannaka duality theorem for bialgebroids generaliz…
Monoidal Morita equivalence
K. Szlachanyi
The monoidal version of classical Morita theory is a theory of bialgebroids. To make this explicit we construct a bicategory the objects of which are the bialgebroids and in which…
The double algebraic view of finite quantum groupoids
Kornel Szlachanyi
This is an introduction to double algebras which is the structure modelled by the properties of the convolution product in Hopf algebras, weak Hopf algebras and in Hopf algebroids.…
Hopf Algebroid Symmetry of Abstract Frobenius Extensions of Depth 2
Gabriella B"ohm, Korn'el Szlach'anyi
We study Frobenius 1-morphisms in an additive bicategory $\c$ satisfying the depth 2 condition. We show that the 2-endomorphism rings $\c^2(ı\x\ib,ı\x\ib)$ and $\c^2(\ib\xı,\ib…
Adjointable monoidal functors and quantum groupoids
K. Szlachanyi
Every monoidal functor G: C --> M has a canonical factorization through the category of bimodules over some monoid R in M such that the factor U: C -->_R M_R is strongly unital. Us…
Galois actions by finite quantum groupoids
K. Szlachanyi
Proposing a certain category of bialgebroid maps we show that the balanced depth 2 extensions appear as they were the finitary Galois extensions in the context of quantum groupoid…
Weak Hopf algebra symmetries of C^*-algebra inclusions
K. Szlachanyi
After a summary on module algebra actions of C^*-weak Hopf algebras we outline the proof of a reconstruction theorem stating that every finite index depth 2 inclusion N < M of unit…
Finite quantum groupoids and inclusions of finite type
K. Szlachanyi
Bialgebroids, separable bialgebroids, and weak Hopf algebras are compared from a categorical point of view. Then properties of weak Hopf algebras and their applications to finite i…
Weak Hopf Algebras II: Representation theory, dimensions and the Markov trace
G. Bohm, K. Szlachanyi
If A is a weak C^*-Hopf algebra then the category of finite dimensional unitary representations of A is a monoidal C^*-category with monoidal unit being the GNS representation D_ep…
Weak C^*-Hopf Algebras and Multiplicative Isometries
G. Bohm, K. Szlachanyi
We show how the data of a finite dimensional weak C^*-Hopf algebra can be encoded into a pair (H,V) where H is a finite dimensional Hilbert space and V: H øH --> H øH is a partial…
Weak Hopf Algebras and Reducible Jones Inclusions of Depth 2. I: From Crossed products to Jones towers
Florian Nill, Kornel Szlachanyi, Hans-Werner Wiesbrock
We apply the theory of finite dimensional weak C^*-Hopf algebras A as developed by G. Böhm, F. Nill and K. Szlachányi to study reducible inclusion triples of von-Neumann algebras N…
Weak Hopf Algebras I: Integral Theory and C^*-structure
G. Bohm, F. Nill, K. Szlachanyi
We give an introduction to the theory of weak Hopf algebras proposed recently as a coassociative alternative of weak quasi-Hopf algebras. We follow an axiomatic approach keeping as…