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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. and directed diagrams yield the same undirected diagram, correspondingly named * Finite Dynkin diagrams *

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  • Dynkin diagram
  • Diagramas de Dynkin
  • Диаграмма Дынкина
  • Diagrama de Dynkin
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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. and directed diagrams yield the same undirected diagram, correspondingly named * Finite Dynkin diagrams *
  • En el campo matemático de la teoría de Lie, un diagrama de Dynkin, nombrado en honor de Eugene Dynkin, es un tipo de gráfico con algunos bordes dobles o triples (dibujado como una línea doble o triple). Los bordes son múltiples, dentro de ciertos límites. El principal interés en los diagramas de Dynkin es como un medio para clasificar las álgebras semisimples de Lie sobre campos algebraicamente cerrados. Esto da lugar a grupos de Weyl, es decir, a muchos (aunque no todos) los grupos de reflexión finitos. Los diagramas de Dynkin también pueden surgir en otros contextos. y * *
  • No campo matemático da teoria de Lie, um diagrama de Dynkin, nomeado por Eugene Dynkin, é um tipo de grafo em que as arestas podem ser simples, duplas ou triplas (o número de ligações entre os mesmos vértices). Quando não são simples, as arestas são orientadas. O principal interesse em diagramas de Dynkin são como uma forma de classificar álgebras de Lie semissimples sobre corpos algebricamente fechados. Isto dá origem a grupos de Weyl, ou seja, a vários (mas não todos) grupos de reflexão finita. Os diagramas de Dynkin também podem surgir noutros contextos. * Diagrama de Dynkin finitos *
  • Диаграмма Дынкина или схема Дынкина, названная именем Евгения Борисовича Дынкина, — это вид графов, в которых некоторые рёбра удвоены или утроены (рисуется как двойная или тройная линия). Кратные рёбра, с некоторыми ограничениями, являются ориентированными. Основной интерес в диаграммах Дынкина заключается в том, что они позволяют ввести классификацию полупростых алгебр Ли над алгебраически замкнутыми полями. Диаграммы приводят к группам Вейля, то есть ко многим (хотя не ко всем) конечным группам отражений. Диаграммы Дынкина возникают также и в других контекстах. и * Конечные диаграммы Дынкина *
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