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 monoid...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 Frobenius–Schur 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.展开更多
基金We thank Professor Siu-Hung Ng for helpful conversations.Z.Y.Wan is supported by the Shuimu Tsinghua Scholar Program.
文摘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 Frobenius–Schur 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.
