ADE classification

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In mathematics, the ADE classification is the complete list of simply laced Lie groups or other mathematical objects satisfying analogous axioms. The list comprises

$A_n,\ D_n,\ E_6,\ E_7,\ E_8$ .

Here $A n$ is the algebra of $S U (n + 1)$ ; $D n$ is the algebra of $S O (2 n)$ , while $E k$ are three of five exceptional compact Lie algebras.

The same classification applies to discrete subgroups of $S U (2)$ , the binary polyhedral groups. The orbifold of $C 2$ constructed using each discrete subgroup leads to an ADE-type singularity at the origin, specifically a Du Val singularity.

The A, D, E nomenclature is shared by the finite Coxeter groups, and the elementary catastrophes. There are deep connections between the three.