Pre-modular fusion categories of small global dimensions

Abstract

We first prove an analogue of Lagrange theorem for global dimensions of fusion categories, then we give a complete classifications of pre-modular fusion categories of integer global dimensions less than or equal to $10$.

arXiv comment19pages

References in corpus (5)

• Frobenius-Schur Indicators and Exponents of Spherical Categories
• Congruence Property In Conformal Field Theory
• Algebraic number fields generated by Frobenius-Perron dimensions in fusion rings
• Classification of Rank 6 Modular Categories with Galois Group $⟨(012)(345)⟩$
• Classification of super-modular categories