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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 formulated 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 An, Bn, Cn, Dn, 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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Dante-Gabryell MonsonThe Lie group E8 has dimension 248. Its rank, which is the dimension of its maximal torus, is 8. Therefore the vectors of the root system are in eight-dimensional Euclidean space: they are described explicitly later in this article. The Weyl group of E8, which is the group of symmetries of the maximal torus which are induced by conjugations in the whole group, has order 696729600.
Mathematics Wikipedia ReferenceMaps for:mbauwens for:srose for:meinhard for:thomaskalka for:joe_edelman for:guaka processdimensions patterns geometry
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05 Jan 89
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