I am new to Lie Algebra. Could someone help me to answer this question? thanks!
Question: how to prove for any non-abelian arbitrary lie algebra $L$, the dimension of it center $Z(L)$ is less or equal to dimension of $L-2$. i.e to prove $$ dim(Z(L)) \leqslant dim(L)-2 $$
The hint is to construct a contradiction by hypothesizing $$ dim(Z(L)) \geqslant dim(L)-1 $$
Could someone give me more suggestions or hints?
Thank you in advance!