Orbifold equivalent potentials

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To a graded finite-rank matrix factorisation of the difference of two homogeneous potentials one can assign two numbers, the left and right quantum dimension. The existence of such a matrix factorisation with non-zero quantum dimensions defines an equivalence relation between potentials, giving rise to non-obvious equivalences of categories. Restricted to ADE singularities, the resulting equivalence classes of potentials are those of type Ad₋₁ for d odd, Ad₋₁,Dd/₂₊₁ for d even but not in 12,18,30, and A₁₁, D₇, E₆, A₁₇, D₁₀, E₇ and A₂₉, D₁₆, E₈. This is the result expected from two-dimensional rational conformal field theory, and it directly leads to new descriptions of and relations between the associated (derived) categories of matrix factorisations and Dynkin quiver representations.