Braid gaugings and categorical invariants

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 $\mathrm{Rep}(D(G))\cong \mathcal{Z}({\text{Vec}}_G)$, whose braid gaugings are studied in-depth.

41 pages; v2: title change to reflect generalizations to categorical setting. Previous version had an error this version fixes. The error lead to the erroneous assertion that "exotic quasitriangular structures" exist for D(G) when G is purely non-abelian. They don't. Results on such matters have been corrected and strengthened to give full braided tensor equivalences