Semidirect products of C*-quantum groups: multiplicative unitaries approach

Abstract

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.

v2: corrected typos

References in corpus (5)

• Quantum group-twisted tensor products of C*-algebras
• Quantum group-twisted tensor products of C*-algebras II
• The Drinfeld double for C*-algebraic quantum groups
• Quantum groups with projection and extensions of locally compact quantum groups
• Generalized fixed point algebras for coactions of locally compact quantum groups

Cited by in corpus (4)

• Quantum $E(2)$ groups for complex deformation parameters
• Braided free orthogonal quantum groups
• New products and ${\mathbb{Z}}_2$-extensions of compact matrix quantum groups
• Braided quantum groups and their bosonizations in the $C^{\ast }$-algebraic framework