A quadrilateral in the Asaeda-Haagerup category

TL;DR

This paper constructs a noncommuting quadrilateral of factors involving the Asaeda-Haagerup subfactor, demonstrating a new structure within the subfactor category by establishing the existence of a specific Q-system.

Contribution

It introduces a novel noncommuting quadrilateral of factors with Asaeda-Haagerup subfactors, expanding the understanding of subfactor categories and their algebraic structures.

Findings

Existence of a Q-system in the Asaeda-Haagerup category with a specific index

Construction of a noncommuting quadrilateral of factors involving Asaeda-Haagerup subfactors

Identification of new algebraic structures within the subfactor category

Abstract

We construct a noncommuting quadrilateral of factors whose upper sides are each the Asaeda-Haagerup subfactor with index $\frac{5+\sqrt{17}}{2} $ by showing the existence of a Q-system in the Asaeda-Haagerup category with index $\frac{7+\sqrt{17}}{2} $.