ADE classification
In mathematics, the ADE classification (originally A-D-E classifications) is a situation where certain kinds of objects are in correspondence with simply laced Dynkin diagrams. The question of giving a common origin to these classifications, rather than a posteriori verification of a parallelism, was posed in. The complete list of simply laced Dynkin diagrams comprises Here "simply laced" means that there are no multiple edges, which corresponds to all simple roots in the root system forming angles of (no edge between the vertices) or (single edge between the vertices). These are two of the four families of Dynkin diagrams (omitting and ), and three of the five exceptional Dynkin diagrams (omitting and ). This list is non-redundant if one takes for If one extends the families to include redundant terms, one obtains the exceptional isomorphisms and corresponding isomorphisms of classified objects. The A, D, E nomenclature also yields the simply laced finite Coxeter groups, by the same diagrams: in this case the Dynkin diagrams exactly coincide with the Coxeter diagrams, as there are no multiple edges. (Wikipedia).
