Double group construction of quantum groups in the von Neumann algebra framework

Abstract

We introduce a notion of double group construction within the category of quasi Woronowicz algebras which are regarded as quantum groups in the von Neumann algebra framework. We show that the quantum double in this setting is always unimodular. The Kac-Takesaki operator of the double group is explicitly described. It is also proven that the dual of the quantum double has a quasitriangular structure.