# A quadrilateral in the Asaeda–Haagerup category

### Marta Asaeda

University of California, Riverside, USACardiff University, Wales, UK

## 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 $\frac{7+\sqrt{17}}{2}$ . We also conjecture the existence of a Q-system in the same category with index $\frac{9+ \sqrt{17}}{2}$ and an associated quadrilateral whose upper sides have index $\frac{7+\sqrt{17}}{2}$ .

## Cite this article

Marta Asaeda, , A quadrilateral in the Asaeda–Haagerup category. Quantum Topol. 2 (2011), no. 3, pp. 269–300

DOI 10.4171/QT/22