The reformulated image conjecture for the deformed polynomial algebra

For $t\in\mathbb C$, let $\mathcal B_t[\xi,z]$ be the algebra on the vector space $\mathbb C[\xi,z]$ with product $\ast_t$, and set

$$\xi\mathbb C[\xi,z]:=\sum_{i=1}^n\xi_i\mathbb C[\xi,z].$$

A subspace of a commutative algebra is a Mathieu subspace if every element whose positive powers lie in the subspace has, after multiplication by any fixed algebra element, all sufficiently large powers still in the subspace. The reformulated image conjecture. For every $t\in\mathbb C$, $\xi\mathbb C[\xi,z]$, regarded as a subspace of $\mathcal B_t[\xi,z]$, is a Mathieu subspace of $\mathcal B_t[\xi,z]$. This is presented as an equivalent reformulation of the image conjecture, connecting that conjecture with the deformation of the polynomial algebra; its status is not resolved in the source.