Solvable Lie Algebra

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.

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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Rowland, Todd. "Solvable Lie Algebra." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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