Bialynicki-Birula-type linearization conjecture for torus actions on free algebras

Let $F_n$ be the free associative algebra on $n$ generators, and let $\mathbb{T}_{n-1}$ be the $(n-1)$-dimensional algebraic torus. An action is linearizable when it is conjugate to a linear action on the generating space by an automorphism of $F_n$. Free-algebra torus linearization conjecture. Any effective action of $\mathbb{T}_{n-1}$ on $F_n$ is linearizable. This is proposed as an analogue of the commutative Bialynicki-Birula linearization theorem; the supplied text gives no proof or resolution.