The noncommutative Shephard–Todd–Chevalley conjecture for quantum polynomial rings

Let $B$ be a quantum polynomial ring and let $G$ be a finite subgroup of $\operatorname{Aut_{gr}}(B)$. Noncommutative Shephard–Todd–Chevalley conjecture. The fixed subring $B^G$ has finite global dimension if and only if $G$ is generated by quasi-reflections. This conjecture proposes a generalization of the classical Shephard–Todd–Chevalley theorem from commutative polynomial rings to quantum polynomial rings; the paper proves the assertion for skew polynomial rings, while the stated generalization remains open here.