|Dept.||University of Warsaw|
I will present a very personal account of the development of the theory of quantum groups on the operator algebra level (limiting my presentation to the C*-algebraic viewpoint). To that end I will give a short introduction to the theory of compact quantum groups with the main focus on the quantum SU(2) group. Next I will shift focus to the non-compact example of the quantum E(2) group which we will place in the scope of the theory of manageable mulitiplicative unitary operators. I will finish with a brief account of the theory of quantum groups defined by such multiplicative unitaries.