En (Lie algebra)
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- The correct title of this article is En (Lie algebra). It features superscript or subscript characters that are substituted or omitted because of technical limitations.
In mathematics, especially in Lie theory, En is the Kac–Moody algebra whose Dynkin diagram is a line of n-1 points with an extra point attached to the third point from the end.
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[edit] Finite dimensional Lie algebras
- E3 is another name for the Lie algebra A1A2 of dimension 11.
- E4 is another name for the Lie algebra A4 of dimension 24.
- E5 is another name for the Lie algebra D5 of dimension 45.
- E6 is the exceptional Lie algebra of dimension 78.
- E7 is the exceptional Lie algebra of dimension 133.
- E8 is the exceptional Lie algebra of dimension 248.
[edit] Infinite dimensional Lie algebras
- E9 is another name for the infinite dimensional affine Lie algebra E8(1) corresponding to the Lie algebra of type E8
- E10 is an infinite dimensional Kac–Moody algebra whose root lattice is the even Lorentzian unimodular lattice II9,1 of dimension 10. Some of its root multiplicities have been calculated; for small roots the multiplicities seem to be well behaved, but for larger roots the observed patterns break down.
- E11 is an infinite dimensional Kac–Moody algebra that has been conjectured to generate the symmetry "group" of M-theory.
- En for n≥12 is an infinite dimensional Kac–Moody algebra that has not been studied much.
[edit] Other Lie algebras named En
- E7½ is a name given to a certain Lie algebra of dimension 190.
[edit] References
- R.W. Gebert, H. Nicolai (1994). "E10 for beginners." . Guersey Memorial Conference Proceedings '94
- P.C. West (2001). "E11 and M Theory." . Class.Quant.Grav. 18 (2001) 4443-4460
