En (Lie algebra)

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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.
E_n for n≥11 is an infinite dimensional Kac–Moody algebra that has not been studied much.

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