Аннотация
The N -commutatorand only if N = n 2 + 2n -2.This is proved for n = 2 and confirmed by computer experiments for n < 5.Under 2-and 5-commutators the algebra of divergence-free vector fields in two dimensions is an sh-Lie (strong homotopic Lie) algebra in the sense of Stasheff.Similarly, W (2) is an sh-Lie algebra with respect to 2-and 6-commutators.