Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Free dynamical quantum groups and the dynamical quantum group $SU^{dyn}_{Q}(2)$

100%

Timmermann T.

Banach Center Publications

2012

tom 98

nr 1

311-341

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.

Multiplier Hopf algebroids arising from weak multiplier Hopf algebras

63%

Timmermann T., Van Daele A.

Banach Center Publications

2015

tom 106

nr 1

73-110

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 natural to investigate the expected link between weak multiplier Hopf algebras and multiplier Hopf algebroids. This relation has been considered already in the original paper on multiplier Hopf algebroids. In this note, we investigate the connection further. First we show that any regular weak multiplier Hopf algebra gives rise, in a natural way, to a regular multiplier Hopf algebroid. Secondly we give a characterization, mainly in terms of the base algebra, for a regular multiplier Hopf algebroid to have an underlying weak multiplier Hopf algebra. We illustrate this result with some examples. In particular, we give examples of multiplier Hopf algebroids that do not arise from a weak multiplier Hopf algebra.

Ograniczanie wyników

2 Banach Center Publications

2 Timmermann T.

1 Van Daele A.

1 2015

1 2012

Wyniki wyszukiwania

Free dynamical quantum groups and the dynamical quantum group $SU^{dyn}_{Q}(2)$

Multiplier Hopf algebroids arising from weak multiplier Hopf algebras