where there are formula_88 terms in the tensor product, and formula_268 is a completely symmetric tensor of order formula_88 belonging to the adjoint representation. That is, formula_268 can be (should be) thought of as an element of formula_271 Recall that the adjoint representation is given directly by the structure constants, and so an explicit indexed form of the above equations can be given, in terms of the Lie algebra basis; this is originally a theorem of Israel Gel'fand. That is, from formula_272, it follows that