Derived isomorphism conjecture for finite-dimensional Lie algebras

Let $\mathfrak{g}_1$ and $\mathfrak{g}_2$ be finite-dimensional Lie algebras over $\mathbb{C}$, and let $\mathfrak{U}\mathfrak{g}_1$ and $\mathfrak{U}\mathfrak{g}_2$ denote their enveloping algebras. Derived isomorphism conjecture. If the derived categories of bounded complexes of $\mathfrak{U}\mathfrak{g}_1$-modules and $\mathfrak{U}\mathfrak{g}_2$-modules are equivalent, then

$$\mathfrak{g}_1\cong\mathfrak{g}_2.$$

The corresponding isomorphism problem for enveloping algebras is widely open in general, although it has a positive answer for semisimple and low-dimensional nilpotent Lie algebras. This derived version asks whether the bounded derived category determines a finite-dimensional complex Lie algebra.