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E8 Expressway (Japan)
E8 may refer to: Mathematics * E8, an exceptional simple Lie group with root lattice of rank 8 * E8 lattice, special lattice in R8 * E8 manifold, mathematical object with no smooth structure or topological triangulation * E8 polytope, alternate name for the 421 semiregular (uniform) polytope * Elementary abelian group of order 8 Physics * E8 Theory, term sometimes loosely used to refer to ''An Exceptionally Simple Theory of Everything'' Transport * E-8 Joint STARS, a retired USAF command and control aircraft * EMD E8, 1949 diesel passenger train locomotive * European route E8, part of the international E-road network, running between Tromsø, Norway and Turku, Finland * European walking route E8, a walking route from Ireland to Turkey * HMS E8, 1912 British E class submarine * London Buses route E8, runs between Ealing Broadway station and Brentford * Mikoyan-Gurevich Ye-8, 1962 supersonic jet fighter developed in the Soviet Union * E8, IATA code for the former A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8. The designation E8 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled A''n'', B''n'', C''n'', D''n'', and five exceptional cases labeled G2, F4, E6, E7, and E8. The E8 algebra is the largest and most complicated of these exceptional cases. Basic description The Lie group E8 has dimension 248. Its rank, which is the dimension of its maximal torus, is eight. 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 that are induced by conjugations in the whole group, has order 2357 = . The compact group E8 is u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
