Braidings for Non-Split Tambara-Yamagami Categories over the Reals

TL;DR

This paper investigates which non-split real Tambara-Yamagami categories admit braidings, classifies their braided equivalence classes, and presents new results on split real and complex Tambara-Yamagami categories.

Contribution

It provides a classification of braidings in non-split real Tambara-Yamagami categories and new insights into split real and complex cases.

Findings

Identified which non-split real Tambara-Yamagami categories admit braidings.

Classified the braided equivalence classes of these categories.

Proved new results about split real and split complex Tambara-Yamagami categories.

Abstract

Non-split Real Tambara-Yamagami categories are a family of fusion categories over the real numbers that were recently introduced and classified by Plavnik, Sanford, and Sconce. We consider which of these categories admit braidings, and classify the resulting braided equivalence classes. We also prove some new results about the split real and split complex Tambara-Yamagami Categories. V2: Final Section removed, to appear in Transformation Groups.