As we said, a homomorphism of Lie algebras is simply a linear mapping between them that preserves the bracket. I want to check, though, that this behaves in certain nice ways.
First off, there is a Lie algebra $latex 0$. That is, the trivial vector space can be given a (unique) Lie algebra structure, and every Lie algebra has a unique homomorphism $latex L\to0$ and a unique homomorphism $latex 0\to L$.
in Turing's on permutations paper, he refers (upon editing) to normalizers, idealizers etc. We can get a feel for what these are:- (the ideal is a bit like the 0, in Hs = 0 for LDPCs)
