Classifying braidings on fusion categories

TL;DR

This paper establishes a classification method for braidings on fusion categories by relating them to specific subcategories of the center, enabling analysis of non-degenerate and group-theoretical cases.

Contribution

It introduces a novel correspondence between braidings and fusion subcategories of the center, providing a new approach to classify braidings on fusion categories.

Findings

Braidings correspond to fusion subcategories of the center transversal to the Lagrangian algebra.

Classification of braidings on non-degenerate fusion categories achieved.

Classification of braidings on group-theoretical fusion categories achieved.

Abstract

We show that braidings on a fusion category $\mathcal{C}$ correspond to certain fusion subcategories of the center of $\mathcal{C}$ transversal to the canonical Lagrangian algebra. This allows to classify braidings on non-degenerate and group-theoretical fusion categories.