Article
YetterDrinfeld modules over weak Hopf algebras and the center construction
10/2004;
Source: arXiv

Article: Quantum groupoids with projection
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ABSTRACT: In this survey we explain in detail how Radford's ideas and results about Hopf algebras with projection can be generalized to quantum groupoids in a strict symmetric monoidal category with split idempotents.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we study the projections of weak braided Hopf algebras using the notion of YetterDrinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study of the structure of weak Hopf algebras with a projection in a braiding setting obtaining a categorical equivalence between the category of weak Hopf algebra projections associated with a weak Hopf algebra H living in a braided monoidal category and the category of Hopf algebras in the nonstrict braided monoidal category of leftleft YetterDrinfeld modules over H.Science China Mathematics 01/2011; 54(5):877906. · 0.71 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In a previous paper, the authors introduced the monoidal category of left–left Yetter–Drinfeld modules over a weak braided Hopf algebra in a strict monoidal category. The main goal of this work is to define the categories of right–right, left–right and right–left Yetter–Drinfeld modules over a weak braided Hopf algebra and prove that there exists a categorical equivalence between all of them. We also establish the categorical equivalences by changing the weak braided Hopf algebra D by its (co)opposite. Finally, the general results are illustrated with an example coming from the projections of weak braided Hopf algebras.Arabian Journal of Mathematics. 01/2013; 2(1).
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