A Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. Any nilpotent Lie algebra is also solvable. The basic example of a nilpotent Lie algebra is the vector space of strictly upper triangular matrices, such as the Lie algebra of the Heisenberg group.

Lie algebra | Lie algebra commutator series | Lie algebra lower central series | Lie algebra representation | Lie group | nilpotent Lie group | solvable Lie group | unipotent

Marius Sophus Lie