Upper central series of a Lie algebra
= Upper central series of a Lie algebra
{title2=$Z_0=0,\quad Z_{i+1}/Z_i=Z(\mathfrak g/Z_i)$}
Each term is the preimage of the <center of a Lie algebra> after quotienting by the preceding term. Equivalently, $Z_{i+1}=\{x:[\mathfrak g,x]\subseteq Z_i\}$. A <Lie algebra> is nilpotent exactly when this series reaches the whole algebra after finitely many steps. For the <Heisenberg Lie algebra>, the series is $0\subset\mathbb Cc\subset\mathfrak g$.