Free dynamical quantum groups and the dynamical quantum group $\mathrm{SU}^{\mathrm{dyn}}_{Q}(2)$
Volume 98 / 2012
Banach Center Publications 98 (2012), 311-341
MSC: Primary 81R50; Secondary 16T05, 46L99.
DOI: 10.4064/bc98-0-14
Abstract
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 $\mathrm{SU}_{q}(2)$ studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.
