Definition in lecture 14

[wildenthal]

The definition of an algebra being "semisimple if it contains no non-trivial abelian ideals" on line 41 should be changed to "semi-simple if it contains no non-zero abelian ideals", or, mirroring the first phrase, "semi-simple if it is non-abelian and it contains no non-trivial ideals". Otherwise, remark 14.2 wouldn't make sense; as it stands, the one-dimensional Lie algebra si semisimple because it has no non-trivial ideals (in particular, no-nontrivial abelian ideals).

[wildenthal]

Well, with my correction, remark 14.2 be tautological. The reason one-dimensional Lie algebras are not simple (nor semisimple) is that they do not behave like other simple Lie algebras: https://math.stackexchange.com/questions/1683787/why-do-we-require-that-a-simple-lie-algebra-be-non-abelian