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Quantum Topology

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Volume 2, Issue 3, 2011, pp. 269–300
DOI: 10.4171/QT/22

Published online: 2011-07-06

A quadrilateral in the Asaeda–Haagerup category

Marta Asaeda[1]

(1) University of California, Riverside, USA

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} $.

Keywords: Subfactors, fusion categories

Asaeda Marta: A quadrilateral in the Asaeda–Haagerup category. Quantum Topol. 2 (2011), 269-300. doi: 10.4171/QT/22