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In mathematics, the ADE classification (originally ''A-D-E'' classifications) is the complete list of simply laced Dynkin diagrams or other mathematical objects satisfying analogous axioms; "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). The list comprises : These comprise 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 question of giving a common origin to these classifications, rather than a posteriori verification of a parallelism, was posed in . 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. == Lie algebras == In terms of complex semisimple Lie algebras: * corresponds to the special linear Lie algebra of traceless operators, * corresponds to the even special orthogonal Lie algebra of even-dimensional skew-symmetric operators, and * are three of the five exceptional Lie algebras. In terms of compact Lie algebras and corresponding simply laced Lie groups: * corresponds to the algebra of the special unitary group * corresponds to the algebra of the even projective special orthogonal group , while * are three of five exceptional compact Lie algebras. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「ADE classification」の詳細全文を読む スポンサード リンク
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