Classification of Spherical Fusion Categories of Frobenius-Schur Exponent 2

• 作者: Zheyan Wan Yilong Wang
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 39-50
• 页数: 12页
• 语种: 英文
• DOI: 10.1142/S1005386721000055

摘要

In this paper,we propose a new approach towards the classification of spherical fusion categories by their Frobenius-Schur exponents.We classify spherical fusion categories of Frobenius-Schur exponent 2 up to monoidal equivalence.We also classify modular categories of Frobenius-Schur exponent 2 up to braided monoidal equivalence.It turns out that the Gauss sum is a complete invariant for modular categories of FrobeniusSchur exponent 2.This result can be viewed as a categorical analog of Arf's theorem on the classification of non-degenerate quadratic forms over fields of characteristic 2.