A Lie algebra 
is solvable when its 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 every
time two such matrices commute, their nonzero entries move further from the diagonal.
Solvable Lie Algebra
See also
Borel Subalgebra, Lie Algebra, Lie Algebra Commutator Series, Lie Algebra Representation, Lie Group, Nilpotent Lie Group, Nilpotent Lie Algebra, Solvable Lie Group, Solvable Lie Group Representation, Split Solvable Lie AlgebraThis entry contributed by Todd Rowland
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Rowland, Todd. "Solvable Lie Algebra." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SolvableLieAlgebra.html