Nilpotent Lie algebra

In mathematics, a Lie algebra is nilpotent if its lower central series eventually becomes zero.

It is a Lie algebra analog of a nilpotent group.

Let ${\displaystyle {\mathfrak {g}}}$ be a Lie algebra. Then ${\displaystyle {\mathfrak {g}}}$ is nilpotent if the lower central series terminates, i.e. if ${\displaystyle {\mathfrak {g}}_{n}=0}$ for some n ∈ ℕ.

...
Wikipedia