In mathematics, an exceptional Lie algebra is a
complexsimple Lie algebra whose
Dynkin diagram is of exceptional (nonclassical) type.[1] There are exactly five of them: ; their respective dimensions are 14, 52, 78, 133, 248.[2] The corresponding diagrams are:[3]
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: