ADE classification

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