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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
- An,Dn,E6,E7,E8.
Here An is the algebra of SU(n + 1); Dn is the algebra of SO(2n), while Ek 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
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details