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 Algebra
*This entry contributed by Todd
Rowland*

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## Cite this as:

Rowland, Todd. "Solvable Lie Algebra." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/SolvableLieAlgebra.html