| Résume | If $A$ is a unital separable $C^*$-algebra, $A\otimes\mathcal K$ denotes the stabilization of $A$, and $\mathcal Q(A\otimes\mathcal K)$ its corona algebra. If and $A$ embeds unitally into $M_n(B)$ for some $n$, we can construct an embedding of $\mathcal Q(A\otimes \mathcal K)$ into $\mathcal Q(B\otimes\mathcal K)$. Is this the only case possible? Namely, if $\mathcal Q(A\otimes\mathcal K)$ embeds into $\mathcal Q(B\otimes\mathcal K)$, is it necessary that $A$ embeds into an amplification of $B$? We study this question and see how the answer depend on the set theoretical axioms one assumes. |
