Braided quantum SU(2) groups

TL;DR

This paper constructs a family of q-deformations of the SU(2) group, extending known quantum groups to complex parameters and introducing braided structures for non-real q, enriching the theory of quantum symmetries.

Contribution

It introduces a new family of q-deformations of SU(2) for complex q, including braided quantum groups for non-real q, expanding the landscape of quantum group theory.

Findings

For real q, recovers Woronowicz's SU_q(2)

For complex q, constructs braided quantum SU(2)

Provides new examples of braided quantum groups

Abstract

We construct a family of q-deformations of SU(2) for complex parameters q not equal to 0. For real q, the deformation coincides with Woronowicz' compact quantum SU_q(2) group. For q not real, SU_q(2) is only a braided compact quantum group with respect to a certain tensor product functor for C*-algebras with an action of the circle group.