ADE classification
From Free net encyclopedia
In mathematics, the ADE classification is the complete list of simply laced Lie 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.
The A, D, E nomeculture is shared by the finite Coxeter groups, and the Elementary_catastrophes. There are deep connections between the three.
[edit]
