ADE classification

Encyclopedia : A : AD : ADE : 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 [SU(n+1)]; [D_n] is the algebra of [SO(2n)], while [E_k] are three of five exceptional compact Lie algebras.

The same classification applies to discrete subgroups of [SU(2)]. The orbifold of [C^2] constructed using each discrete subgroup leads to an ADE-type singularity at the origin.

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

See also

• Dynkin diagram
• String theory
• E6 (mathematics)
• E7 (mathematics)
• E8 (mathematics)
• Elliptic surface
• Quiver

References

• [A Rapid Introduction to ADE Theory], John McKay

 

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