Weak Hopf algebras and quantum groupoids

P. Schauenburg

P. Schauenburg

Banach Center Publications, Tome 60 (2003), p. 171-188 / Harvested from The Polish Digital Mathematics Library

Résumé

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 separable. We extend the comparison to cover module and comodule theory, duality, and the question when a bialgebroid should be called a Hopf algebroid.

Publié le : 2003-01-01

Zbl 1064.16041

EUDML-ID : urn:eudml:doc:282475

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     author = {P. Schauenburg},
     title = {Weak Hopf algebras and quantum groupoids},
     journal = {Banach Center Publications},
     volume = {60},
     year = {2003},
     pages = {171-188},
     zbl = {1064.16041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-12}
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P. Schauenburg. Weak Hopf algebras and quantum groupoids. Banach Center Publications, Tome 60 (2003) pp. 171-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-12/