On braided fusion categories I

TL;DR

This paper introduces the concept of the core of a braided fusion category, distinguishing the non-group-like part, and provides a comprehensive exposition of known results without assuming pre-modularity or non-degeneracy.

Contribution

It defines the core of a braided fusion category and offers a self-contained overview of existing results, emphasizing the analogy with Casimir Lie algebras.

Findings

Definition of the core of a braided fusion category

Separation of non-group-like components in braided fusion categories

Comprehensive exposition of known results without assuming pre-modularity

Abstract

This work is a detailed version of arXiv:0704.0195 [math.QA]. We introduce a new notion of the core of a braided fusion category. It allows to separate the part of a braided fusion category that does not come from finite groups. We also give a comprehensive and self-contained exposition of the known results on braided fusion categories without assuming them pre-modular or non-degenerate. The guiding heuristic principle of our work is an analogy between braided fusion categories and Casimir Lie algebras.