On Grothedieck rings of rank 4 self-dual fusion categories

2025/05/25 by Jingcheng Dong, Dong, Jingcheng
Mathematics · #18D10 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2505.19153

openalex publication_date 2025/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \C be a self-dual fusion category of rank 4 which has a nontrivial proper fusion subcategory. We identify three new families of Grothendieck rings for \C: one of them is completely determined, the other two are parameterized by several non-negative integers.

Citations

• Non-trivially graded self-dual fusion categories of rank 4
• Pseudo-unitary non-self-dual fusion categories of rank 4
• On braided fusion categories I
• On braided fusion categories I
• Weakly group-theoretical and solvable fusion categories
• Fusion categories of rank 2
• On fusion categories
• Module categories, weak Hopf algebras and modular invariants

Related

• Pseudo-unitary non-self-dual fusion categories of rank 4
• Non-trivially graded self-dual fusion categories of rank 4
• Pivotal fusion categories of rank 3 (with an Appendix written jointly with Dmitri Nikshych)
• Classifying integral Grothendieck rings up to rank 5 and beyond
• Burnside type results for fusion categories