Angiono–Azevedo–Heckenberger conjecture on finite root systems

Let $V$ be a braided vector space of diagonal type, with braiding matrix $\mathfrak{q}=(q_{ij})$ and Nichols algebra $\mathscr{B}_{\mathfrak{q}}$. A Nichols algebra has finite root system in the sense of the classification of Nichols algebras of diagonal type.

Angiono–Azevedo–Heckenberger conjecture. If $\mathscr{B}_{\mathfrak{q}}$ has finite Gelfand–Kirillov dimension, then its root system is finite.

Finite-dimensional Nichols algebras of diagonal type already have finite root systems, and the conjecture extends this phenomenon to all finite-Gelfand–Kirillov-dimensional cases. The statement was verified in various cases, but the source does not establish it in full generality.