He did this quite independently of Lie (and not it would appear in a manner which Lie found satisfactory), and it was Cartan who completed the classification of semisimple Lie algebras in 1900.
Siya did ito lubos na malaya ng humiga / magsinungaling (at hindi ito ay lalabas sa isang paraan na kung saan humiga / magsinungaling natagpuan ang kasiya-siya), at ito ay Cartan na natapos na ang pag-uuri ng semisimple humiga / magsinungaling algebras sa 1900.