Braided free orthogonal quantum groups

TL;DR

This paper introduces new braided quantum groups over the circle group, generalizing free orthogonal quantum groups and braided quantum SU(2), with detailed analysis of their representations and equivalences.

Contribution

It constructs novel braided quantum groups over the circle group, extending the theory of free orthogonal quantum groups and braided quantum SU(2).

Findings

Constructed braided quantum groups over the circle group.

Described irreducible representations and fusion rules.

Analyzed conditions for monoidal equivalence.

Abstract

We construct some braided quantum groups over the circle group. These are analogous to the free orthogonal quantum groups and generalise the braided quantum SU(2) groups for complex deformation parameter. We describe their irreducible representations and fusion rules and study when they are monoidally equivalent.