Composed inclusions of $A_3$ and $A_4$ subfactors

Abstract

In this article, we classify all standard invariants that can arise from a composed inclusion of an $A_3$ with an $A_4$ subfactor. More precisely, if $\mathcal{N}\subset \mathcal{P}$ is the $A_3$ subfactor and $\mathcal{P}\subset \mathcal{M}$ is the $A_4$ subfactor, then only four standard invariants can arise from the composed inclusion $\mathcal{N}\subset \mathcal{M}$. This answers a question posed by Bisch and Haagerup in 1994. The techniques of this paper also show that there are exactly four standard invariants for the composed inclusion of two $A_4$ subfactors.

49 pages, 33 figures

References in corpus (4)

• The classification of subfactors of index at most 5
• Subfactors of index less than 5, part 3: quadruple points
• Calculating two-strand jellyfish relations
• The little desert? Some subfactors with index in the interval (5,3+\sqrt{5})

Cited by in corpus (10)

• The classification of subfactors of index at most 5
• Q-system completion for C* 2-categories
• 2-supertransitive subfactors at index $3+\sqrt{5}$
• Calculating two-strand jellyfish relations
• Drinfeld centers of fusion categories arising from generalized Haagerup subfactors
• Quantum invariants of deformed Fourier matrices
• Classification of $\mathbb{Z}/2\mathbb{Z}$-quadratic unitary fusion categories
• Block maps and Fourier analysis
• A complete classification of unitary fusion categories tensor generated by an object of dimension $\frac{1+\sqrt{5}}{2}$
• Discrete Inclusions of C*-algebras