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

The isomorphism problem for universal enveloping algebras of nilpotent Lie algebras