A Lie algebra g is solvable when its Lie algebra commutator series, or derived series, g^k vanishes for some k. Any nilpotent Lie algebra is solvable. The basic example is the vector space of upper triangular matrices, because every time two such matrices commute, their nonzero entries move further from the diagonal.

Lie algebra | Lie algebra commutator series | Lie algebra representation | Lie group | nilpotent Lie algebra | nilpotent Lie group | solvable Lie group