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arXiv · 1308.5691

Composed inclusions of $A_3$ and $A_4$ subfactors

Zhengwei Liu
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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.

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Zhengwei Liu. 2013-08-26. Composed inclusions of $A_3$ and $A_4$ subfactors. https://doi.org/10.1016/j.aim.2015.03.017

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