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

TL;DR

This paper explores the structure of C*-quantum groups with projection, showing they can be uniquely decomposed into simpler components using manageable multiplicative unitaries, extending Radford's theorem to the C*-algebra setting.

Contribution

It provides a new decomposition framework for C*-quantum groups with projection based on manageable multiplicative unitaries, generalizing Radford's theorem.

Findings

Unique decomposition of C*-quantum groups with projection

Extension of Radford's theorem to the C*-algebra context

Use of manageable multiplicative unitaries for structural analysis

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.