Semidirect Products of C -Quantum Groups: Multiplicative Unitaries Approach

C -quantum groups with projection are the noncommutative analogues of semidirect products of groups. Radford's Theorem about Hopf algebras with projection suggests that any C -quantum group with projection decomposes uniquely into an ordinary C -quantum group and a "braided" C -quantum group. We establish this on the level of manageable multiplicative unitaries.