The isomorphism problem for universal enveloping algebras of nilpotent Lie algebras

Details The isomorphism problem for universal enveloping algebras of nilpotent Lie algebras The isomorphism problem for universal enveloping algebras of nilpotent Lie algebras

2010-06-07

arxiv.org/abs/1006.1341v1

Mathematics

Rings and Algebras

Scientific paper

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.

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