Trace trilinear form of a Lie algebra representation ($B(X,Y,Z)$)

For a finite-dimensional representation $d$, the trilinear form $B(X,Y,Z)=\mathrm{Tr}(d(X)d(Y)d(Z))$ is invariant under simultaneous adjoint action. This follows by writing the sum of its three infinitesimal variations as the trace of a commutator.