The Sierra–Walton conjecture on Noetherian enveloping algebras

Let $K$ be a field of characteristic zero, let $\mathfrak{g}$ be a Lie algebra over $K$, and let $U(\mathfrak{g})$ denote its universal enveloping algebra. Sierra–Walton conjecture. If $\mathfrak{g}$ is infinite dimensional, then $U(\mathfrak{g})$ is not Noetherian.

This conjecture asserts that a Noetherian universal enveloping algebra can arise only from a finite-dimensional Lie algebra. The paper introduces weakly Noetherian Lie algebras to study this question; the supplied text does not state that the conjecture has been resolved.