Exceptional Lie Algebra

A Lie algebra over an algebraically closed field is called exceptional if it is constructed from one of the root systems E_6, E_7, E_8, F_4, and G_2 by the Chevalley construction (Humphreys 1977). If the field has field characteristic other than 2 or 3, than such Lie algebras are all simple (Steinberg 1961, p. 1120).

The exceptional Lie algebras over an arbitrary field are those corresponding to the same list of root systems as well as some corresponding to the root system of type D_4 and the phenomenon of triality. Algebras of this last type occur over some fields (finite fields, number fields) and not others (the real numbers, algebraically closed fields).

See also

Lie Algebra, Simple Lie Algebra

This entry contributed by Skip Garibaldi

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Jacobson, N. Exceptional Lie Algebras. New York: Dekker, 1971.Humphreys, J. E. §25 in Introduction to Lie Algebras and Representation Theory, 3rd ed. New York: Springer-Verlag, 1977.Steinberg, R. "Automorphisms of Classical Lie Algebras." Pacific J. Math. 11, 1119-1129, 1961.

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Exceptional Lie Algebra

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Garibaldi, Skip. "Exceptional Lie Algebra." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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