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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-10, author = {Piotr Stachura}, title = {From double Lie groups to quantum groups}, journal = {Fundamenta Mathematicae}, volume = {185}, year = {2005}, pages = {195-240}, zbl = {1085.22001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-10} }
Piotr Stachura. From double Lie groups to quantum groups. Fundamenta Mathematicae, Tome 185 (2005) pp. 195-240. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-10/