Exceptional Lie algebra

In mathematics, an exceptional Lie algebra is a complex simple Lie algebra whose Dynkin diagram is of exceptional (nonclassical) type. There are exactly five of them: formula_1; their respective dimensions are 14, 52, 78, 133, 248. The corresponding diagrams are:
In contrast, simple Lie algebras that are not exceptional are called classical Lie algebras (there are infinitely many of them).
Construction.
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: