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In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). The multiple edges are, within certain constraints, directed. The main interest in Dynkin diagrams are as a means to classify semisimple Lie algebras over algebraically closed fields. This gives rise to Weyl groups, i.e. to many (although not all) finite reflection groups. Dynkin diagrams may also arise in other contexts. The term "Dynkin diagram" can be ambiguous. In some cases, Dynkin diagrams are assumed to be directed, in which case they correspond to root systems and semi-simple Lie algebras, while in other cases they are assumed to be undirected, in which case they correspond to Weyl groups; the and directed diagrams yield the same undirected diagram, correspondingly named In this article, "Dynkin diagram" means ''directed'' Dynkin diagram, and ''undirected'' Dynkin diagrams will be explicitly so named. Image:Finite Dynkin diagrams.svg|Finite Dynkin diagrams Image:Affine Dynkin diagrams.png|Affine (extended) Dynkin diagrams == Classification of semisimple Lie algebras == The fundamental interest in Dynkin diagrams is that they classify semisimple Lie algebras over algebraically closed fields. One classifies such Lie algebras via their root system, which can be represented by a Dynkin diagram. One then classifies Dynkin diagrams according to the constraints they must satisfy, as described below. Dropping the direction on the graph edges corresponds to replacing a root system by the finite reflection group it generates, the so-called Weyl group, and thus undirected Dynkin diagrams classify Weyl groups. 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「Dynkin diagram」の詳細全文を読む スポンサード リンク
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