
## 11. Fusion categories from subfactors

1. #### Problem 11.1.

[Snyder] Can you classify all algebras in fusion categories with small Frobenius-Perron dimension (e.g., less than $3+\sqrt{3}$)?
• #### Problem 11.2.

[Peters] Compute the center of the even half of the Asaeda-Haagerup and extended Haagerup subfactors.
• #### Problem 11.2.

[Morrison, Penneys] Is there a conceptual construction of the even half of 4442?
The even half of 4442 looks like a copy of the even part of affine $E_6$ fusion category (it is also $\text{Rep}(A_4)$) and another copy of affine $E_6$, but as a module category. It looks like $\text{Rep}(A_4)$, graded by the Fibonacci category.

Cite this as: AimPL: Classifying fusion categories, available at http://aimpl.org/fusioncat.