Noncommutative Auslander correspondence for semisimple Hopf actions

Let $H$ be a semisimple Hopf algebra and let $A$ be a noetherian Artin–Schelter regular, connected graded algebra generated in degree one. Suppose that $A$ is a graded $H$-module algebra with an inner faithful action and trivial homological determinant, and that $A^H\neq A$. Here $A\# H$ denotes the smash product and $\operatorname{End}_{A^H}(A)$ the endomorphism algebra of $A$ as a right $A^H$-module. Noncommutative Auslander conjecture. There is a natural graded algebra isomorphism

$$A\# H\cong \operatorname{End}_{A^H}(A).$$

This conjecture extends Auslander's theorem from small finite-group actions on commutative polynomial rings to semisimple Hopf actions on noetherian AS regular algebras. Its status is not established in the supplied text.