A nilpotent Lie algebra is a Lie algebra whose Lie algebra lower central series 
vanishes for
some 
.
Any nilpotent Lie algebra is also solvable.
A basic example is the Lie algebra of strictly
upper triangular matrices of a fixed size, with the commutator
as its Lie bracket. The Lie
algebra of the Heisenberg group is an example
of this type.
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, Nilpotence, Nilpotent Lie Group, Real Form, 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