En (Lie algebra)

In mathematics, E_n 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.

E_7½ is a name for a certain Lie algebra of dimension 190.

Examples

• 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.
• 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 II_9,1 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.
• E_n for n≥12 is an infinite dimensional Kac–Moody algebra that has not been studied much.

References

• R.W. Gebert, H. Nicolai (1994). "E₁₀ for beginners". arXiv:hep-th/9411188. {{cite arXiv}}: Cite has empty unknown parameter: |version= (help) Guersey Memorial Conference Proceedings '94
• P.C. West (2001). "E₁₁ and M Theory". arXiv:hep-th/0104081. {{cite arXiv}}: Cite has empty unknown parameter: |version= (help) Class.Quant.Grav. 18 (2001) 4443-4460