5.2 Simple-Ideal Decomposition of Semisimple Lie Algebras

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In this video, we show that a semisimple lie algebra can be decomposed into the direct sum of its simple ideals. Here is a reference for in addition to the book:

ideal decomposition lie algebra lie algebras representation theory semisimple

Advika Rajapakse
Thank you, it was wonderful watching your videos
Thank you very much for the videos. I have one question about the first part of the proof. Couldn't we have used the fact that the killing form is nondegenerate to prove that $I+I^{\\perp}=L$ ?