Noetherian enveloping algebras of simple graded Lie algebras

Nicol\'as Andruskiewitsch; Olivier Mathieu

Noetherian enveloping algebras of simple graded Lie algebras

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arxiv 2405.15235 v2 pith:VCRZRXA2 submitted 2024-05-24 math.RA

Nicolás Andruskiewitsch , Olivier Mathieu This is my paper · ORCID

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keywords algebraalgebrasenvelopinggradednoetheriansimplefinite-dimensionalmathbb

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abstract

It is shown that if the universal enveloping algebra of a simple $\mathbb Z^n$-graded Lie algebra is Noetherian, then the Lie algebra is finite-dimensional.

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Enveloping algebras of derivations of commutative and noncommutative algebras
math.RA 2024-11 conditional novelty 7.0 of 10

The universal enveloping algebra of the Lie algebra of derivations of any infinite-dimensional finitely generated algebra over a characteristic zero field is not noetherian.

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