= Killing form of a nilpotent Lie algebra vanishes
{c}
{title2=$\kappa\equiv0$}
Every <Adjoint representation> operator raises the <lower central series of a Lie algebra> filtration. In a basis adapted to that finite filtration, all adjoint operators are strictly triangular. Their products have zero trace, so the <Killing form> vanishes. Consequently its <radical of the Killing form> is the whole algebra. For strictly upper triangular matrices the filtration can be seen directly by the gap between the column and row indices.
// Target: algebra.bigb
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