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We consider products of structure constants of a finite-dimensional compact simple Lie algebra, in which all indices except a few are contracted in pairs. We prove that such a product is zero if only one index is free, is proportional to the Cartan-Killing tensor if two indices are free and is proportional to a structure constant itself if three indices are free. For SU(n),n?3 we also consider products of usuald (related to the anti-commutator) and structure constantsf. The results for one and two free indices are still valid. For three free indices the product is proportional to either anf or ad according to whether the number off's in the product is odd or even.

A property of the structure constants of finite dimensional compact simple Lie algebras