Examples of locally compact quantum groups through the bicrossed product construction

TL;DR

This paper introduces simple examples of non-compact locally compact quantum groups using the bicrossed product construction, making complex quantum group examples more accessible to non-specialists.

Contribution

It provides new, straightforward examples of non-compact locally compact quantum groups via the bicrossed product method, simplifying their construction.

Findings

Examples are easier to understand and construct.

Demonstrates the utility of bicrossed product in quantum group theory.

Highlights the importance of these examples for non-specialized audiences.

Abstract

The main aim of this paper is to introduce some examples of non-compact locally compact quantum groups to a non-specialized audience. The major importance of these examples is their simplicity. Other examples as the quantum E(2) group of Woronowicz are much more difficult to construct. We will make use of the bicrossed product construction to obtain our examples. This construction dates back to Kac, Takeuchi and Majid. It was also considered by Baaj & Skandalis.