The Drinfeld double for C*-algebraic quantum groups

TL;DR

This paper explores the duality between the generalized Drinfeld double and quantum codouble in the context of C*-algebraic quantum groups, expanding the theoretical framework beyond regular cases.

Contribution

It establishes the duality between the generalized Drinfeld double and quantum codouble for modular or manageable multiplicative unitaries, broadening previous regularity assumptions.

Findings

Duality between generalized Drinfeld double and quantum codouble proven.

Properties of these dualities discussed within the framework of modular or manageable unitaries.

Extends the theory to non-regular cases in C*-algebraic quantum groups.

Abstract

In this article, we establish the duality between the generalised Drinfeld double and generalised quantum codouble within the framework of modular or manageable (not necessarily regular) multiplicative unitaries, and discuss several properties.