The Embedding Problem in Algebras with Involution

Let $K$ be an algebraically closed field of characteristic zero, and let $A$ and $B$ be two simple algebras with involution over $K$. In this note we study the embedding problem for algebras with involution. More specifically, if the algebra $A$ satisfies the polynomial identities with involution of the algebra $B$, we investigate whether there exists an embedding of $A$ into $B$ that preserves the involutions.