A nilpotent Lie algebra is a Lie algebra whose Lie algebra lower central series 
vanishes for some 
. Any nilpotent Lie algebra is also solvable.
The basic example of a nilpotent Lie algebra is the vector
space of strictly upper triangular
matrices, such as the Lie algebra of the Heisenberg
group.
Nilpotent Lie Algebra
See also
Lie Algebra, Lie Algebra Commutator Series, Lie Algebra Lower Central Series, Lie Algebra Representation, Lie Algebra Upper Central Series, Lie Group, Nilpotent Lie Group, Solvable Lie Group, UnipotentThis entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Nilpotent Lie Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NilpotentLieAlgebra.html