ADE classification
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In mathematics, the ADE classification is the complete list of simply laced groups or other mathematical objects satisfying analogous axioms. The list comprises
- <math>A_n,D_n,E_6,E_7,E_8<math>.
Here <math>A_n<math> is the algebra of <math>SU(n+1)<math>; <math>D_n<math> is the algebra of <math>SO(2n)<math>, while <math>E_k<math> are three of five exceptional compact Lie algebras.
The same classification applies to discrete subgroups of <math>SU(2)<math>. The orbifold of <math>C^2<math> constructed using each discrete subgroup leads to an ADE-type singularity at the origin. String theory offers an explanation why these two apparently different occurrences of ADE classification match: type IIA string theory compactified on an ADE-type singularity leads to the enhanced gauge symmetry with the same name.