What exactly is lower central series of Lie algebra?

Question

I've read several definitions of $LCS$ and derived series of Lie algebra, but I'm not sure if i get it right: In case of $LCS$, the relationship is given as $g_{k+1}=[g,g_k]$, does $``g_k"$ stand for $k$-th generator? And could someone kindly provide an example of such relationship for an $su(N)$ in matrix representation?