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 Cquantum 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.