The second Brauer–Thrall conjecture for tau-tilting infinite algebras

Let $A$ be a finite-dimensional algebra. A module $V\in\operatorname{mod}(A)$ is a brick if its endomorphism algebra is a division algebra. The algebra $A$ is tau-tilting infinite if it has infinitely many support tau-tilting modules.

Second Brauer–Thrall conjecture. If $A$ is tau-tilting infinite, then there exists a dimension $d\geq 0$ and infinitely many pairwise non-isomorphic bricks $V\in\operatorname{mod}(A)$ with $\dim(V)=d$.

This is a tau-tilted version of the second Brauer–Thrall conjecture. The paper notes that the theorem proved for affine GLS algebras confirms this conjecture for that class, while the general assertion remains open.