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\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

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.