The symplectic lie algebra defined by $sp\left(n\right)=\left\{ X\in gl_{2n}\,|\, X^{t}J+JX=0\right\}$ when $J=\begin{pmatrix}0 & I\\ -I & 0\end{pmatrix}$. So $X\in sp\left(n\right)$ is of the sort $X=\begin{pmatrix}A & B\\ C & -A^{t}\end{pmatrix}$ when $B=B^{t},\, C=C^{t}$.
This far I was able to get, but how can I prove that it is simple?
Thanks!