Lipman–Rosenberg conjecture on Dixmier–Douady invariants of nilpotent Lie groups

Let $\mathsf{G}$ be a connected nilpotent Lie group, and let $A$ be a continuous trace subquotient of $C^*(\mathsf{G})$, meaning a subquotient whose spectrum $\hat{A}\subseteq\hat{\mathsf{G}}$ is Hausdorff. Denote its Dixmier–Douady invariant by $\delta_{\rm DD}(A)$. Lipman–Rosenberg conjecture. For every such $\mathsf{G}$ and $A$, one has

$$\delta_{\rm DD}(A)=0.$$

If true, this would ensure that continuous trace subquotients arising from connected nilpotent Lie groups admit no nontrivial Dixmier–Douady obstruction; the supplied text presents this as a conjecture and does not state a resolution.