Pseudo-unitary non-self-dual fusion categories of rank 4

2014/01/09 by Hannah K. Larson, Larson, Hannah K. · 2 citations
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.1401.1879

arxiv created 2014/10/30 · arxiv updated 2014/10/31

Abstract

A fusion category of rank 4 has either four self-dual objects or exactly two self-dual objects. We study fusion categories of rank 4 with exactly two self-dual objects, giving nearly a complete classification of those based ring that admit pseudo-unitary categorification. More precisely, we show that if C is such a fusion category, then its Grothendieck ring K(C) must be one of seven based rings, six of which have know categorifications. In doing so, we classify all based rings associated with near-group categories of the group ℤ/3ℤ.

Cited by

• On Grothedieck rings of rank 4 self-dual fusion categories
• Hypergraph Characterization of Fusion Rings
• Classification of some ℤ/2ℤ× ℤ/2ℤ-quadratic fusion categories of rank 6

Related

• On Grothedieck rings of rank 4 self-dual fusion categories
• Non-trivially graded self-dual fusion categories of rank 4
• Non-pseudounitary fusion
• Interpolated family of non-group-like simple integral fusion rings of Lie type
• Pivotal fusion categories of rank 3 (with an Appendix written jointly with Dmitri Nikshych)