2

If $Y$ is a vector subspace of the Lie algebra $\mathfrak{g}$ and $n_1,n_2\in N_\mathfrak{g}(Y)$ does the following hold?

$$[n_1,[n_2,Y]]=[n_1,A]=B$$ where $B\subseteq A\subseteq Y$

So many hats
  • 450
  • Well, $[n_1,[n_2,Y]]\subseteq [n_1,Y]\subseteq Y$. What are your $A$ and $B$ exactly? If they're just any two random vector subspaces with $B\subseteq A\subseteq Y$, then of course not. – anon Aug 17 '15 at 06:15
  • @anon Oh wow that is much cleaner... My sets were just placeholders pretty much for that purpose. – So many hats Aug 17 '15 at 06:16

1 Answers1

0

The idea that you are looking for is that $[n_1,[n_2,Y]]\subseteq [n_1,Y] \subseteq Y$ Your placeholders hold, but in the abstract case they can't be found of course.

So many hats
  • 450