Finite quantum groupoids and inclusions of finite type

By Korn'el Szlach'anyi. 2000

78 citations recorded by the source corpus.

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 index and finite depth inclusions of von Neumann algebras are shortly reviewed. A hint is given at a duality between bialgebroid actions and abstract inclusions in 2-categories.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3fe2e57a6ea0d265e309ec504b535f0fa091cd78

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Tensor categories: a selective guided tour (2008, background): “Szlachányi [252]: An R-fiber functor on C gives rise to an equivalence C ≃ A−Mod for a weak Hopf algebra (with base R).”
Bialgebroids, ×A-Bialgebras and Duality☆ (2002, background): “Xu [21], while (B3) in this form appears in [19] (in a slightly different convention though).”
Hopf algebroids with bijective antipodes: Axioms, integrals, and duals (2003, background): “Left (right) bialgebroids can be characterized by the property that the forgetful fu AM → LML (MA → RMR) is strong monoidal [17,20].”
Hopf Algebroids (2008, methodology): “In [64], [41] and [68] also the converse is proven: a k-module map ǫ : R → k on the base algebra R of a bialgebroid B, with normalised dual basis ∑ i ei ⊗k fi ∈ R ⊗k R, determines a weak bialgebra structure on the underlying k-module B.”
The monoidal Eilenberg–Moore construction and bialgebroids (2002, background): “The motivating example of bimonads is associated to a Takeuchi ×R-algebra [28], also called bialgebroid [12, 5, 22, 26].”
Module categories, weak Hopf algebras and modular invariants (2001, methodology): “This is indeed true and the corresponding structure on H is a structure of a weak bialgebra, see [ 34 ].”