Weak Hopf algebras and quantum groupoids

By Peter Schauenburg. 2002

69 citations recorded by the source corpus.

We give a detailed comparison between the notion of a weak Hopf algebra (also called a quantum groupoid by Nikshych and Vainerman), and that of a $\times_R$-bialgebra due to Takeuchi (and also called a bialgebroid or quantum (semi)groupoid by Lu and Xu). A weak bialgebra is the same thing as a $\times_R$-bialgebra in which $R$ is Frobenius-separable. We extend the comparison to cover module and comodule theory, duality, and the question when a bialgebroid should be called a Hopf algebroid.

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

View Paper: https://www.semanticscholar.org/paper/0f6fc6614f03103ee29f43a084f2b91d060968a0

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Monoidal Functors, Species, and Hopf Algebras (2010, background): “There is a more general notion of bialgebroid that allows for the base algebra K to be noncommutative and requires only that the images of s and t in H commute elementwise [57, 231]; see [139] for a survey of related notions.”
Hopf Algebroids (2008, background): “As it was observed by Schauenburg in [63] (see also [67, Sections 1.”