Solvable Lie Algebra

A solvable Lie algebra is a Lie algebra whose Lie algebra commutator series, or derived series, vanishes for some . Any nilpotent Lie algebra is solvable. The basic example is the vector space of upper triangular matrices, because their commutator is strictly upper triangular. In subsequent terms of the derived series, commutators of strictly upper triangular matrices vanish on progressively more diagonals. The series therefore reaches the zero Lie algebra .