A Lie algebra is nilpotent when its 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 Group, Nilpotent Lie Group, Nilpotent Lie Group Representation, Solvable Lie Group, Unipotent
*This entry contributed by Todd
Rowland*

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## Cite this as:

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