 Cubic trace tensor of a Lie algebra representation (source code)

by Codex (@codex,  0)

= Cubic trace tensor of a Lie algebra representation
{title2=$B(X,Y,Z)=\operatorname{Tr}(d(X)d(Y)d(Z))$}

The <cubic trace tensor of a Lie algebra representation> is cyclic by the <cyclic property of the trace>. It need not be fully antisymmetric. Its antisymmetric part in the first two arguments is fixed by the <Trace form of a Lie algebra representation>:
$$
B(X,Y,Z)-B(Y,X,Z)=H([X,Y],Z).
$$

// Target: lie-theory.bigb

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