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Free dynamical quantum groups and the dynamical quantum group $S U_{Q}^{d y n} (2)$

Thomas Timmermann — 2012

Banach Center Publications

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 $S U_{q} (2)$ studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.

Multiplier Hopf algebroids arising from weak multiplier Hopf algebras

Thomas Timmermann; Alfons Van Daele — 2015

Banach Center Publications

It is well-known that any weak Hopf algebra gives rise to a Hopf algebroid. Moreover it is possible to characterize those Hopf algebroids that arise in this way. Recently, the notion of a weak Hopf algebra has been extended to the case of algebras without identity. This led to the theory of weak multiplier Hopf algebras. Similarly also the theory of Hopf algebroids was recently developed for algebras without identity. They are called multiplier Hopf algebroids. Then it is quite...

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Free dynamical quantum groups and the dynamical quantum group S U Q d y n ( 2 )

Multiplier Hopf algebroids arising from weak multiplier Hopf algebras

Free dynamical quantum groups and the dynamical quantum group $S U_{Q}^{d y n} (2)$