ADE classification

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

A_n,D_n,E₆,E₇,E₈.

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 C² 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.

See also

• Dynkin diagram
• String theory
• E6 (mathematics)
• E7 (mathematics)
• E8 (mathematics)

See also: ADE classification, Dynkin diagram, E6 (mathematics), E7 (mathematics), E8 (mathematics), Gauge symmetry, Mathematics, Orbifold, Simply laced group