Conjecture on cancellation for prime algebras of low center or dimension three

Let $\operatorname{char}(\operatorname{\Bbbk})=0$, and let $A$ be a noetherian finitely generated prime algebra.

Cancellation conjecture.

1. If $\operatorname{GKdim}(Z(A))\leq 1$, then $A$ is cancellative.
2. If $\operatorname{GKdim}(A)=3$ and $A$ is not PI, then $A$ is cancellative.

These assertions propose broad cancellation criteria for noncommutative algebras, extending the preceding results for particular classes of AS-regular and PI algebras. Their resolution is not specified in the source.