The derived isomorphism conjecture for enveloping algebras

Let $\mathfrak{g}$ and $\mathfrak{g'}$ be finite-dimensional Lie algebras over $\mathbb{C}$. Write $U(\mathfrak{g})$ for the enveloping algebra of $\mathfrak{g}$, and likewise for $\mathfrak{g'}$. Derived isomorphism conjecture. If the derived categories of bounded complexes of $U(\mathfrak{g})$-modules and $U(\mathfrak{g'})$-modules are equivalent, then

$$\mathfrak{g}\cong \mathfrak{g'}.$$

This is a derived analogue of the isomorphism problem for enveloping algebras, which asks whether an isomorphism of enveloping algebras determines an isomorphism of the underlying Lie algebras. The paper states that certain classes, including Frobenius Lie algebras, are derived invariants of their enveloping algebras, while the conjecture remains open in general.