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There is no simple universally accepted way to construct exceptional Lie algebras; in fact, they were discovered only in the process of the classification program. Here are some constructions:
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190:{\displaystyle {\mathfrak {g}}_{2},{\mathfrak {f}}_{4},{\mathfrak {e}}_{6},{\mathfrak {e}}_{7},{\mathfrak {e}}_{8}}
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Exceptional Lie algebras may be realized as the derivation algebras of appropriate nonassociative algebras.
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has given a uniformed construction of the five exceptional Lie algebras.
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In contrast, simple Lie algebras that are not exceptional are called
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619:References
529:Construct
756:246650103
658:, § 21.2.
716:(1991).
694:9 August
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