@Andrews As a very rough draft, I would propose something like the following for the tag description:

> A simple Lie algebra is non-abelian Lie algebra with no nontrivial ideals. A semisimple Lie algebra is a Lie algebra which is the direct sum of simple Lie algebras. This tag is for questions about semisimple Lie algebras, including their classification and correspondent to root systems and Dynkin diagrams.

For for the tag wiki:

> A simple Lie algebra is non-abelian Lie algebra $\mathfrak{g}$ whose only ideals are $\{0\}$ and $\mathfrak{g}$. A semisimple Lie algebra is a Lie algebra which is the direct sum of simple Lie algebras. Every finite dimensional Lie algebra can be decomposed as the semidirect product of a solvable ideal and a semisimple subalgebra (this is the Levi decomposition).

> Semisimple Lie algebras over an algebraically closed field are completely classified by their root systems) which, in turn, correspond to a collection of Dynkin diagrams. This, together with the Levi decomposition, make semisimple Lie algebras objects of interest in representation theory.

Does this seem like a reasonable starting place to you?

@XanderHenderson I will just add that this is how the tag-excerpt and tag-wiki looked like before the tag was deleted: math.stackexchange.com/posts/3179233/revisions and math.stackexchange.com/posts/3179232/revisions

Perhaps this would be a bit more on topic in the tagging chat room. But I suppose the mods won't mind a slight digression. (And if they do, they can always move the messages there.)

@MartinSleziak I must have known that there was a tagging room, but I had plumb forgotten about it. Since the conversation last happened here, I poked Andrew here. Thanks for the links. Now I feel like I have wasted 15 minutes of my time. :\

:P