The classification of subfactors with index at most $5 \frac{1}{4}$

TL;DR

This paper completes the classification of subfactor standard invariants for indices up to 5.25, including the first composite index, advancing understanding of quantum symmetries in operator algebras.

Contribution

It provides the full classification of subfactor invariants up to index 5.25, covering new cases with composite indices, expanding the known landscape of quantum symmetries.

Findings

Complete classification of subfactor invariants up to index 5.25

Identification of the first interesting composite index at 3+√5

Enhanced understanding of quantum symmetries in subfactors

Abstract

Subfactor standard invariants encode quantum symmetries. The small index subfactor classification program has been a rich source of interesting quantum symmetries. We give the complete classification of subfactor standard invariants to index $5\frac{1}{4}$, which includes $3+\sqrt{5}$, the first interesting composite index.