Cocycle twisting of semidirect products and transmutation

Abstract

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.

22 pages; v3: some corrections, classification of braided free orthogonal quantum groups up to isomorphism added; v2: minor corrections and improvements, a discussion of Mrozinski's quantum groups added

References in corpus (1)

• Braided quantum symmetries of graph ${\mathrm{C}}^{\ast }$-algebras

Cited by in corpus (1)

• Braided quantum symmetries of graph ${\mathrm{C}}^{\ast }$-algebras