On the Complexity of Lie Algebras - Groote, Hans F. de (1987)
Let U, V, W be finite dimensional vector spaces over a field k and let : U x V → W be a bilinear mapping. The (multiplieative) complexity L(~) of ~ is defined as the least r ∈~ such that there are linear forms Ul,...,u r , Vl,...,v r ∈ (U xV) and elements Wl,...,w r ∈ W satisfying r ~(x,y) = ~ Up(X,y) Vp(X,y) Wp for all (x~y) ∈ U× V .