Identities in Lie algebras of vector fields (Q919444)

The author studies the identities of infinite dimensional Lie algebras of vector fields. It is proved that the Lie algebra of Hamiltonian vector fields on the plane does not satisfy any polynomial identity of two variables of degree \(\leq 5\) in one of them. He also obtains the upper bound exp Cn\({}^{2/3}\) for the growth of the Lie algebra generated by two generic Hamiltonian vector fields on the plane.