The Unitary Implementation of a Locally Compact Quantum Group Action

The Unitary Implementation of a Measured Quantum Groupoid Action

In ([L2]), Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In [E5], Lesieur’s axioms have been simplified, and the notions of actions, crossed-product, dual actions, had been introduced and developped; a biduality theorem for actions had been proved. This article continues that program : we prove the existence of a standard implementa...

The Quantum Double of a (locally) Compact Group

We generalise the quantum double construction of Drinfel’d to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the ∗-algebra structure of the quantum double. If the conjugacy classes in the group are countably separated, then we classify the irreducible ∗-representations by using the connection with so–called transformation group...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

The study of relation between existence of admissible vectors and amenability and compactness of a locally compact group

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

Unitary Representations of Compact Quantum Groups

Let v be the right regular representation of a compact quantum group G. Then ([6], Proposition 4.4) v contains all irreducible representations of G and each irreducible representation enters v with the multiplicity equal to its dimension. The result is certainly known for classical compact groups ([1]). The aim of this paper is to give a short survey on this subject and to provide a different p...