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E₈ (mathematics)

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Graph of E₈ Gosset polytope, 4_2,1

Coxeter-Dynkin diagram:

The correct title of this article is E₈ (mathematics). It features superscript or subscript characters that are substituted or omitted because of technical limitations.

In mathematics, E₈ is the name given to a family of closely related structures. In particular, it is the name of some exceptional simple Lie algebras as well as that of the associated simple Lie groups. It is also the name given to the corresponding root system, root lattice, and Weyl/Coxeter group, and to some finite simple Chevalley groups . It was discovered between the years of 1888-1890 by Wilhelm Killing.

The designation E₈ comes from Wilhelm Killing and Élie Cartan's classification of the complex simple Lie algebras, which fall into four infinite families labeled A_n , B_n, C_n, D_n, and five exceptional cases labeled E₆, E₇, E₈, F₄, and G₂. The E₈ algebra is the largest and most complicated of these exceptional cases, and is often the last case of various theorems to be proved.

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