Double categories and quantum groupoids

Abstract

We give the construction of a class of weak Hopf algebras (or quantum groupoids) associated to a matched pair of groupoids and certain cocycle data. This generalizes a now well-known construction for Hopf algebras, first studied by G. I. Kac in the sixties. Our approach is based on the notion of double groupoids, as introduced by Ehresmann.

34 pages, amslatex. The statement in Proposition 3.10 has been corrected

References in corpus (2)

• Finite Quantum Groupoids and Their Applications
• Examples of weak Hopf algebras arising from vacant double groupoids

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• On Double Groups and the Poincaré group
• Partial Actions of Weak Hopf Algebras on Coalgebras
• The structure of double groupoids
• On the quiver-theoretical quantum Yang-Baxter equation
• Double groupoid cohomology and extensions
• The Double Category of Paired Dialgebras on the Chu Category
• The double algebraic view of finite quantum groupoids