Editing Semisimple Lie algebra (section)

== History<!--linked from 'Dynkin diagram'--> ==
The semisimple Lie algebras over the complex numbers were first classified by [[Wilhelm Killing]] (1888–90), though his proof lacked rigor. His proof was made rigorous by [[Élie Cartan]] (1894) in his Ph.D. thesis, who also classified semisimple real Lie algebras. This was subsequently refined, and the present classification by Dynkin diagrams was given by then 22-year-old [[Eugene Dynkin]] in 1947. Some minor modifications have been made (notably by J. P. Serre), but the proof is unchanged in its essentials and can be found in any standard reference, such as {{Harv|Humphreys|1972}}.