Weak Hopf algebras and quantum groupoids

P. 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 -