### NON-EXHAUSTIVE LIST OF MATHEMATICAL OBJECTS THAT HAVE AN ADE TYPE CLASSIFICATION

• Simply Laced Complex Simple Lie Algebras (Killing and Cartan 1888-94).
• Finite proper subgroups of $$\mathfrak{sl}_2(\mathbb{C})$$ and the associated Platonic solids (Klein 1884).
• Kleinian singularities (Slodowy 1983).
• Subfactors of a II$$_1$$ factor with finite index (Jones 1983).
• Modular invariants of WZW models associated to $\mathfrak{sl}_2(\mathbb{C})$ (Cappelli, Itzykson and Zuber 1987).
• Finite reflection groups of crystallographic and of simply-laced type (Bourbaki 1981, Humphreys 1990).
• Quivers of finite type (Gabriel 1972).
• Algebraic solutions to the hypergeometric equation (Hille 1976).
• Finite simple module categories over $${\bf TL}(-[2]_q)/\mathcal{N}$$ where $$q$$ is an even root of unity (Ostrik 2001).
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