Hi

let N,L,Q are lie algebras. N is abelian and

Attachment 23538

an exact sequence.

I want to show that N is Q-MOdule . but i can't. if

http://latex.codecogs.com/gif.latex?...%20%5Cpi%20l=q

is it true? but i don't show 3 conditions of modules. 3 conditions are:

http://latex.codecogs.com/gif.latex?...7%7D.%28q.n%29

if

http://latex.codecogs.com/gif.latex?...%20%5Cpi%20l=q

are false, can you tell me q.n=??

thanks.