Cocycle twisting of semidirect products and transmutation

We apply Majid’s transmutation procedure to Hopf algebra maps $H\to \mathbb{C}[T]$, where $T$ is a compact abelian group, and explain how this construction gives rise to braided Hopf algebras over quotients of $T$ by subgroups that are cocentral in $H$. This allows us to unify and generalize a number of recent constructions of braided compact quantum groups, starting from the braided $S{U}_q(2)$ quantum group, and describe their bosonizations.