  In this paper we study the isomorphism problem for the universal enveloping
algebras of nilpotent Lie algebras. We prove that if the characteristic of the
underlying field is not~2 or~3, then the isomorphism type of a nilpotent Lie
algebra of dimension at most~6 is determined by the isomorphism type of its
universal enveloping algebra. Examples show that the restriction on the
characteristic is necessary.
