Simplicity conjecture for nonzero central quotients of the Virasoro enveloping algebra

Let $V\!ir$ be the Virasoro algebra, let $z$ denote its central element, and let $\operatorname{U}(V\!ir)$ be its universal enveloping algebra. The Virasoro central-quotient simplicity conjecture. If $\lambda\neq 0$, then

$$\operatorname{U}(V\!ir)/(z-\lambda)$$

is simple. The analogous symmetric-algebra quotient is Poisson simple, motivating this enveloping-algebra assertion. Its status is not resolved in the supplied text.