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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.
Thomas Timmermann. "Free dynamical quantum groups and the dynamical quantum group $SU^{dyn}_{Q}(2)$." Banach Center Publications 98.1 (2012): 311-341. <http://eudml.org/doc/281638>.
@article{ThomasTimmermann2012, 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 $SU_\{q\}(2)$ studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.}, author = {Thomas Timmermann}, journal = {Banach Center Publications}, keywords = {dynamical quantum group; Hopf algebroid; quantum groupoid}, language = {eng}, number = {1}, pages = {311-341}, title = {Free dynamical quantum groups and the dynamical quantum group $SU^\{dyn\}_\{Q\}(2)$}, url = {http://eudml.org/doc/281638}, volume = {98}, year = {2012}, }
TY - JOUR AU - Thomas Timmermann TI - Free dynamical quantum groups and the dynamical quantum group $SU^{dyn}_{Q}(2)$ JO - Banach Center Publications PY - 2012 VL - 98 IS - 1 SP - 311 EP - 341 AB - 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 $SU_{q}(2)$ studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases. LA - eng KW - dynamical quantum group; Hopf algebroid; quantum groupoid UR - http://eudml.org/doc/281638 ER -