# Weak Hopf algebras and quantum groupoids

Banach Center Publications (2003)

- Volume: 61, Issue: 1, page 171-188
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topP. Schauenburg. "Weak Hopf algebras and quantum groupoids." Banach Center Publications 61.1 (2003): 171-188. <http://eudml.org/doc/282475>.

@article{P2003,

abstract = {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 $×_R$-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 $×_R$-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.},

author = {P. Schauenburg},

journal = {Banach Center Publications},

keywords = {weak Hopf algebras; quantum groupoids; bialgebroids; weak bialgebras; comodules},

language = {eng},

number = {1},

pages = {171-188},

title = {Weak Hopf algebras and quantum groupoids},

url = {http://eudml.org/doc/282475},

volume = {61},

year = {2003},

}

TY - JOUR

AU - P. Schauenburg

TI - Weak Hopf algebras and quantum groupoids

JO - Banach Center Publications

PY - 2003

VL - 61

IS - 1

SP - 171

EP - 188

AB - 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 $×_R$-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 $×_R$-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.

LA - eng

KW - weak Hopf algebras; quantum groupoids; bialgebroids; weak bialgebras; comodules

UR - http://eudml.org/doc/282475

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.