Braid gaugings and categorical invariants

TL;DR

This paper explores the concept of braid gauging in categories, linking it to classical Hopf algebra structures and showing how it reveals new aspects of categorical invariants like fusion rules and Frobenius-Schur indicators.

Contribution

It introduces a Hopf algebraic perspective on braid gauging and applies it to deepen understanding of categorical invariants, especially in the context of representation categories of quantum doubles.

Findings

Braid gauging can alter fusion rules and Frobenius-Schur indicators.

The Hopf algebraic description clarifies the nature of braid gaugings.

In-depth analysis of braid gaugings in Rep(D(G)) category.

Abstract

We study the categorical notion of braid gauging and obtain its classical Hopf algebraic description. We demonstrate how braid gauging can provide new insights on certain categorical invariants, such as the fusion rules and the higher Frobenius-Schur indicators. The running example for the paper is the category $\operatorname{Rep}(D(G))\cong \mathcal{Z}(\text{Vec}_G)$, whose braid gaugings are studied in-depth.