Editing Simple Lie group (section)

===Simple Lie algebras===
{{main|simple Lie algebra}}
The [[Lie group–Lie algebra correspondence|Lie algebra of a simple Lie group]] is a simple Lie algebra. This is a one-to-one correspondence between connected simple Lie groups with [[Triviality (mathematics)|trivial]] center and simple Lie algebras of dimension greater than 1. (Authors differ on whether the one-dimensional Lie algebra should be counted as simple.)

Over the complex numbers the semisimple Lie algebras are classified by their [[Dynkin diagram]]s, of types "ABCDEFG". If ''L'' is a real simple Lie algebra, its complexification is a simple complex Lie algebra, unless ''L'' is already the complexification of a Lie algebra, in which case the complexification of ''L'' is a product of two copies of ''L''. This reduces the problem of classifying the real simple Lie algebras to that of finding all the [[real form]]s of each complex simple Lie algebra (i.e., real Lie algebras whose complexification is the given complex Lie algebra). There are always at least 2 such forms: a split form and a compact form, and there are usually a few others. The different real forms correspond to the classes of automorphisms of order at most 2 of the complex Lie algebra.