Nilpotent Lie Algebra

A Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. 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.

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

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