Makar-Limanov's symmetric free subalgebra conjecture for division rings with involution

Let $D$ be a division ring with center $k$, and let $\ast$ be a $k$-involution on $D$, meaning a $k$-linear map satisfying $(ab)^{\ast}=b^{\ast}a^{\ast}$ and $a^{\ast\ast}=a$ for all $a,b\in D$. An element $a\in D$ is symmetric with respect to $\ast$ when $a^{\ast}=a$.

Makar-Limanov's involutional conjecture. If $D$ is infinite dimensional over $k$ and finitely generated as a division $k$-algebra, then there exist two symmetric elements in $D$ which freely generate a free $k$-subalgebra of $D$.

This is presented as an involutional version of Makar-Limanov's conjecture. The paper describes its results as supporting evidence, so the conjecture remains open in general.