10 citations · 10 across the 3 of their papers we have counts for
11 papers
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.…
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…
Dual Bialgebroids for Depth Two Ring Extensions
L. Kadison, K. Szlachanyi
We introduce a general notion of depth two for ring homomorphism N --> M, and derive Morita equivalence of the step one and three centralizers, R = C_M(N) and C = End_{N-M}(M ø_N M…
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…