The 3-dimensional Heisenberg Lie algebra can be described by the presentation:

$$\mathcal{H}=\big\langle x, y, z\,\big\vert\,[x,y] = z, [x,z]=[y,z]=0\big\rangle$$

The derived subalgebra $[\mathcal{H},\mathcal{H}]$ is a central ideal spanned by $z$, and the whole Lie algebra is a nilpotent Lie algebra (thus not simple or semi-simple).