We introduce dynamical analogues of the free orthogonal and free unitary quantum groups, which are no longer Hopf algebras but Hopf algebroids or quantum groupoids. These objects are constructed on the purely algebraic level and on the level of universal C*-algebras. As an example, we recover the dynamical studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-14,
author = {Thomas Timmermann},
title = {Free dynamical quantum groups and the dynamical quantum group $SU^{dyn}\_{Q}(2)$
},
journal = {Banach Center Publications},
volume = {97},
year = {2012},
pages = {311-341},
zbl = {1272.81099},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-14}
}
Thomas Timmermann. Free dynamical quantum groups and the dynamical quantum group $SU^{dyn}_{Q}(2)$
. Banach Center Publications, Tome 97 (2012) pp. 311-341. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-14/