On cocycle twisting of compact quantum groups

TL;DR

This paper constructs examples of cocycle twists on compact quantum groups that result in non-compact yet locally compact quantum groups, illustrating how twisting can alter the underlying C*-algebra structure.

Contribution

It provides explicit examples of cocycle twisting leading to non-compact quantum groups with changed C*-algebra structures, expanding understanding of quantum group deformations.

Findings

Twisted quantum groups are non-compact but locally compact.

Cocycle twists can change the underlying C*-algebra.

Examples demonstrate new classes of quantum groups.

Abstract

In this article, we give a class of examples of compact quantum groups and unitary 2-cocycles on them, such that the twisted quantum groups are non-compact, but still locally compact quantum groups (in the sense of Kustermans and Vaes). This also provides examples of cocycle twists where the underlying C*-algebra of the quantum group changes.