From double Lie groups to quantum groups
Volume 188 / 2005
Fundamenta Mathematicae 188 (2005), 195-240
MSC: 81R50, 22A22, 22E99.
DOI: 10.4064/fm188-0-10
Abstract
It is shown, using geometric methods, that there is a $C^*$-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
