Rank 4 Premodular Categories

Abstract

We consider the classification problem for rank 4 premodular categories. We uncover a formula for the 2nd Frobenius-Schur indicator of a premodular category, and complete the classification of rank 4 premodular categories (up to Grothendieck equivalence).

Removed appendix due to error in proof. Added journal reference

References in corpus (5)

• From Quantum Groups to Unitary Modular Tensor Categories
• Pivotal fusion categories of rank 3 (with an Appendix written jointly with Dmitri Nikshych)
• On classification of modular tensor categories
• On Higher Frobenius-Schur Indicators
• On the classification of non-self-dual modular categories

Cited by in corpus (8)

• Fermionic Modular Categories and the 16-fold Way
• On classification of modular categories by rank
• Classification of Rank 5 Premodular Categories
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Monoidal categories enriched in braided monoidal categories
• Classification of super-modular categories
• The $F$-Symbols for Transparent Haagerup-Izumi Categories with $G={\mathbb{Z}}_{2n+1}$
• On the Classification of Weakly Integral Modular Categories